Modulo p operation
Given a positive integer p, any integer n must have an equation
n = kp + r
Where K and R are integers and 0 ≤ r
For positive integers p and integers A and B, the following operations are defined:
Modulo operation: A
Http://mathforum.org/library/drmath/view/52343.htmlMod function and negative numbers
Date: 04/28/2000 at 11:17:09From: AnneSubject: Using the mod() function with negative numbersI work in IT - Technical Support. I am trying to sort out a problem for
A ^ B mod C
Assume 0
1. The original method is to first obtain a ^ B and finally mod C.
However, this method is inefficient, and the time complexity is O (B), and a ^ B must be less than N to avoid overflow. It has great limitations.
2.
DescriptionPeople is different. Some secretly read magazines full of interesting girls ' pictures, others create a a-bomb in their cellar, others like USI Ng Windows, and some like difficult mathematical games. Latest Marketing the shows, that's the
Order of integers: set A and n are positive integers of the a^x=1, making the smallest positive integer x (mod n) The order of a modulo n//order Template: A^x=1 (mod M), call Getjie (a,m)//Input: 10^10>a,m>1//output: No solution returned-1, with a
2^X mod n = 1Time limit:2000/1000 MS (java/others) Memory limit:65536/32768 K (java/others)Total submission (s): 13341 Accepted Submission (s): 4143Problem descriptiongive a number n, find the minimum x (x>0) that satisfies 2^x mod n = 1.Inputone
1. Residual: The remainder after the division is divided, for example:
MOD 4 = 2; -17 MOD 4 =-1; -3 MOD 4 =-3; 4 MOD (-3) = 1; -4 MOD 3 =-1;
If a mod B is an XOR, then the resulting symbol is the same as a; Of course, a mod B is equivalent
2^x mod n = 1Time limit:2000/1000 MS (java/others) Memory limit:65536/32768 K (java/others) total submission (s): 12605 Accepted Submission (s): 3926Problem DescriptionGive a number n, find the minimum x (x>0) that satisfies 2^x mod n = 1.InputOne
The beauty of the original root G of the modulo prime p is reflected in the presence of a non-zero number G power of each modulo p. Therefore, for any number 1
G, G ^ 2, G ^ 2, ''', G ^ (P-2), G ^ (pm)
Exactly the same as model a P. The
Ask for the smallest X to make a ^ x = B (mod C)
Question:
[Expand the baby step giant step to solve the discrete logarithm problem]
Author aekdycoin![Normal baby step giant step][Problem model]Solution0 [Idea]We can make an equivalentX = I
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