HDU 1452 Happy 2004 for all factors and functional applications of 2004^n
Last Update:2015-05-12
Source: Internet
Author: User
<span id="Label3"></p><p><p>Topic Link: Click to open the link</p></p><p><p>Baidu a Puzzle: Click to open the link</p></p><p><p></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px">The factor of <span style="font-family:Calibri; word-wrap:normal; word-break:normal">6</span> is <span style="font-family:Calibri; word-wrap:normal; word-break:normal">1,2,3,6;</span> the factor of 6 is <span style="font-family:Calibri; word-wrap:normal; word-break:normal">s (6) =1+2+3+6=12;</span></span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; Color:rgb (70,70,70); font-family:simsun; font-size:14px; Background-color:rgb (229,231,231) "> <span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px"><span style="font-family: Calibri; word-wrap:normal; Word-break:normal ">20 </span> is a factor of <span style=" font-family:calibri; word-wrap:normal; word-break:normal "> 1,2,4,5,10,20; The factor of the </span> is <span style="font-family:calibri; word-wrap:normal; word-break:normal">s (20) =1+2+4+5+10+20 =42; </span> </span> </p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; Color:rgb (70,70,70); font-family:simsun; font-size:14px; Background-color:rgb (229,231,231) "> <span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px"><span style="font-family: Calibri; word-wrap:normal; Word-break:normal ">2 </span> factor is <span style=" font-family:calibri; word-wrap:normal; word-break:normal ">1,2; 2 The factor of the </span> is <span style="font-family:calibri; word-wrap:normal; word-break:normal">s (2) =1+2=3; </span> </span> </p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; Color:rgb (70,70,70); font-family:simsun; font-size:14px; Background-color:rgb (229,231,231) "> <span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px"><span style="font-family: Calibri; word-wrap:normal; Word-break:normal ">3 </span> factor is <span style=" font-family:calibri; word-wrap:normal; word-break:normal ">1,3; 3 The factor of the </span> is <span style="font-family:calibri; word-wrap:normal; word-break:normal">s (3) =1+3=4; </span> </span> </p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; Color:rgb (70,70,70); font-family:simsun; font-size:14px; Background-color:rgb (229,231,231) "> <span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px"><span style="font-family: Calibri; word-wrap:normal; Word-break:normal ">4 </span> Factor and is <span style=" font-family:calibri; word-wrap:normal; word-break:normal ">s (4) =1+2+4=7; </span> </span> </p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px">The factor of <span style="font-family:Calibri; word-wrap:normal; word-break:normal">5</span> and is <span style="font-family:Calibri; word-wrap:normal; word-break:normal">s (5) =1+5=6;</span></span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-family:Calibri; font-size:14px; word-wrap:normal; word-break:normal; line-height:24px">s (6) =s (2) *s (3) =3*4=12;</span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-family:Calibri; font-size:14px; word-wrap:normal; word-break:normal; line-height:24px">s (=s) (4) *s (5) =7*6=42;</span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px">Is this a coincidence?</span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; Color:rgb (70,70,70); font-family:simsun; font-size:14px; Background-color:rgb (229,231,231) "> <span style="font-size:14px word-wrap:normal word-break:normal line-height:24px <span" font-family:calibri; word-wrap:normal; word-break:normal ">s" = 1+2+5+10+25+50=93=3*31=s (2) *s (+), s (+) =1+5+25=31. </span> </p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; Color:rgb (70,70,70); font-family:simsun; font-size:14px; Background-color:rgb (229,231,231) "> <span style=" font-family:calibri; word-wrap:normal; Word-break:normal " this is called the integrable function in number theory when <span>gcd (a, b) =1 </span> <span style="font-family:calibri; word-wrap:normal; word-break:normal">s (a*b) =s (a) *s (b); </span> </p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px">If <span style="font-family:Calibri; word-wrap:normal; word-break:normal">P</span> is a prime number</span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-family:Calibri; font-size:14px; word-wrap:normal; word-break:normal; line-height:24px">s (p^n) =1+p+p^2+...+p^n= (p^ (n+1)-1)/(p-1) (1)</span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px">Example <span style="font-family:Calibri; word-wrap:normal; word-break:normal">hdu1452 Happy 2004</span></span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px">Calculation factor and <span style="font-family:Calibri; word-wrap:normal; word-break:normal">s (2004^x) mod,</span></span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-family:Calibri; font-size:14px; word-wrap:normal; word-break:normal; line-height:24px">2004=2^2 *167</span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-family:Calibri; font-size:14px; word-wrap:normal; word-break:normal; line-height:24px">s (2004^x)) = (s (2^2x))) * (s (3^x))) * (s (167^x)))</span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-family:Calibri; font-size:14px; word-wrap:normal; word-break:normal; line-height:24px">167) = 22;</span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-family:Calibri; font-size:14px; word-wrap:normal; word-break:normal; line-height:24px">s (2004^x)) = (s (2^2x))) * (s (3^x))) * (s (22^x)))</span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; Color:rgb (70,70,70); font-family:simsun; font-size:14px; Background-color:rgb (229,231,231) "> <span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px"><span style="font-family: Calibri; word-wrap:normal; Word-break:normal ">a=s (2^2x) = (2^ (2x+1)-1)//</span> According to (<span style=" font-family:calibri; word-wrap:normal; Word-break:normal ">1 </span>) </span> </p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; Color:rgb (70,70,70); font-family:simsun; font-size:14px; Background-color:rgb (229,231,231) "> <span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px"><span style="font-family: Calibri; word-wrap:normal; Word-break:normal ">b=s (3^x) = (3^ (x+1)-1)/2//</span> According to (<span style=" font-family:calibri; word-wrap:normal; Word-break:normal ">1 </span>) </span> </p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; Color:rgb (70,70,70); font-family:simsun; font-size:14px; Background-color:rgb (229,231,231) "> <span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px"><span style="font-family: Calibri; word-wrap:normal; Word-break:normal ">c=s (22^x) = (22^ (x+1)-1)/21//</span> According to (<span style=" font-family:calibri; word-wrap:normal; Word-break:normal ">1 </span>) </span> </p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; Color:rgb (70,70,70); font-family:simsun; font-size:14px; Background-color:rgb (229,231,231) "> <span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px"><span style="font-family: Calibri; word-wrap:normal; Word-break:normal ">% </span> algorithm <span style=" font-family:calibri; word-wrap:normal; word-break:normal ">1. (a*b)%p= (a%p) * (b%p) </span> </span> </p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; Color:rgb (70,70,70); font-family:simsun; font-size:14px; Background-color:rgb (229,231,231) "> <span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px"><span style="font-family: Calibri; word-wrap:normal; Word-break:normal ">% </span> algorithm <span style=" font-family:calibri; word-wrap:normal; word-break:normal ">2. (a/b)%p= (a *b^ ( -1)%p) </span> </span> </p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; Color:rgb (70,70,70); font-family:simsun; font-size:14px; Background-color:rgb (229,231,231) "> <span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px"><span style="font-family: Calibri; word-wrap:normal; Word-break:normal ">b^ ( -1) </span> is <span style=" font-family:calibri; word-wrap:normal; word-break:normal "> inverse element of b </span> (<span style="font-family:calibri; word-wrap:normal; word-break:normal">%p </span>) </span> </p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; Color:rgb (70,70,70); font-family:simsun; font-size:14px; Background-color:rgb (229,231,231) "> <span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px"><span style="font-family: Calibri; word-wrap:normal; The inverse element of the Word-break:normal ">2 </span> is <span style=" font-family:calibri; word-wrap:normal; word-break:normal ">15 </span> (<span style="font-family:calibri; word-wrap:normal; Word-break:normal" ) < span>), because <span style=" font-family:calibri; word-wrap:normal; Word-break:normal ">2*15=30% 29=1% </span> </span> </span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; Color:rgb (70,70,70); font-family:simsun; font-size:14px; Background-color:rgb (229,231,231) "> <span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px"><span style="font-family: Calibri; word-wrap:normal; The inverse element of the Word-break:normal ">21 </span> is <span style=" font-family:calibri; word-wrap:normal; word-break:normal ">18 </span> (<span style="font-family:calibri; word-wrap:normal; Word-break:normal" ) < span>), because <span style=" font-family:calibri; word-wrap:normal; Word-break:normal ">21*18=378% =1% </span> </span> </span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-size:14px; word-wrap:normal; word-break:normal; line-height:24px">So</span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-family:Calibri; font-size:18px; word-wrap:normal; word-break:normal; line-height:27px">A= (powi (2,2*x+1,29)-1)% 29;</span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-family:Calibri; font-size:18px; word-wrap:normal; word-break:normal; line-height:27px">b= (powi (3,x+1,29)-1) *15% 29;</span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-family:Calibri; font-size:18px; word-wrap:normal; word-break:normal; line-height:27px">c= (powi (22,x+1,29)-1) *18% 29;</span></p></p><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><p style="margin-top:0px; margin-bottom:5px; padding-top:0px; padding-bottom:0px; border:0px; list-style:none; word-wrap:normal; word-break:normal; line-height:21px; color:rgb(70,70,70); font-family:simsun; font-size:14px; background-color:rgb(229,231,231)"><span style="font-family:Calibri; font-size:18px; word-wrap:normal; word-break:normal; line-height:27px">ans= (a*b)% 29*c% 29;</span></p></p><br><p><p></p></p><pre code_snippet_id="664712" snippet_file_name="blog_20150512_1_8824619" name="code" class="cpp">#include <stdio.h> #include <iostream> #include <algorithm> #include <sstream> #include < stdlib.h> #include <string.h> #include <limits.h> #include <vector> #include <string># Include <time.h> #include <math.h> #include <iomanip> #include <queue> #include <stack># Include <set> #include <map>const int inf = 1e8;const double eps = 1e-8;const double pi = acos ( -1.0); template & Lt;class t>inline BOOL Rd (T &ret) {char c; int sgn;if (c = GetChar (), c = = EOF) return 0;while (c! = '-' && (c< ' 0 ' | | c> ' 9 ')) c = GetChar (); sgn = (c = = '-')? -1:1;ret = (c = = '-')? 0: (c-' 0 '); while (c = GetChar (), c >= ' 0 ' &&c <= ' 9 ') ret = ret * + (c-' 0 '); ret *= sgn;return 1;} Template <class t>inline void pt (T x) {if (x <0) {putchar ('-'); x = x;} If (x>9) pt (x/10);p Utchar (x% 10 + ' 0 ');} using namespace std;const int mod = 29;int Pow (int x, int y) {int ans = 1;while (y) {if (y &Amp 1) ans = ans*x%mod;y >>= 1;x = x*x%mod;} Return ans;} int n;//2004= 2*2*3*167int Gao (int x, int y) {int ans = Pow (x, y + 1)-1;while (ans% (x-1)) ans + = mod;ans/= X-1;retu RN ans%mod;} int main () {while (cin>>n, n) {int ans = Gao (2, 2 * n) * Gao (3, n) * Gao (167, n); cout << ans% mod<< endl; }return 0;}</pre><br><br><p><p></p></p><p><p>HDU 1452 Happy 2004 for all factors and functional applications of 2004^n</p></p></span>
