# POJ number theory

Source: Internet
Author: User

1.burnside theorem, Polya counting method
This one can see Brudildi's "Combinatorial Mathematics", the book of this chapter is written in very detailed and easy to understand. It is better to fully understand, understand the problem, do not just remember a formula.
* Simple question: (directly with the set formula can be)
pku2154 Color
* Strongly recommended: (This question is very good, very clever)
pku2888 Magic Bracelet
2. Permutation, permutation operations

The concept of displacement is still better understood, "combinatorial mathematics" inside there is said. For the power of permutation you can refer to the Pan Zhenhao of the "rapid power operation of permutation group", written very well.
* Simple question: (You should understand the concept.)
pku3270 Cow Sorting
pku1026 Cipher
* Permutation power operation:
pku1721 CARDS
pku3128 Leonardo ' s Notebook
* Recommended: (Good app)
pku3590 The Shuffle Problem
3. Prime, integer decomposition, Euler functions

Prime numbers are probably the most timeless and classic problem in number theory (our team name is primemusic^-^). The judgment of prime number, the determination of prime number by sieve method and the judgment of large prime number ... There are many other problems that will use prime numbers.
* The most water and the most water: (When the mood is not good for the boredom of it)
pku1365 Prime Land
pku2034 anti-prime Sequences
pku2739 Sum of consecutive Prime Numbers
pku3518 Prime Gap
pku3126 Prime Path
pku1595 Prime Cuts
pku3641 pseudoprime Numbers
pku2191 Mersenne Composite Numbers
pku1730 Perfect Pth Powers
pku2262 Goldbach ' s conjecture
pku2909 Goldbach ' s conjecture
* Sieve Method:
pku2689 Prime Distance (very good one application)
* Inverse primes:
zoj2562 more divisors
* Prime judgment, Integer decomposition:
These two questions are used to miller_rabin the prime judgment and Pollard_rho integer decomposition, the algorithm book will have, it should belong to the template problem, but it is best to understand their own knock over.
pku1811 Prime Test
pku2429 GCD & LCM Inverse

* Euler functions:
Euler's functions can be used in many places in number theory, which is important.
pku1284 Primitive Roots (theorem on Huangen: the original root of P is Euler (Euler (p)), when P is an odd prime, Euler (p) =p-1, the answer is Euler (p-1))
pku2407 relatives (very water)
pku2773 Happy 2006
pku2478 Farey Sequence (fast Euler function)
pku3090 Visible Lattice Points (Mr Farley series)
* Recommended: (Euler function, Fermat theorem)
pku3358 Period of an Infinite Binary Expansion
* Integer decomposition
This is also very important yes, including the representation of large numbers.
pku2992 divisors
Pku3101 Astronomy (score of least common multiple)
4. Extended Euclidean, linear congruence, Chinese remainder theorem

This should be a more important part of number theory, this kind of topic is also very much, the specific content is best to first look at the number theory book, I have also collated some, you can refer to:
* Simple question:
pku1006 biorhythms
pku1061 the frog's date
pku2891 Strange to Express integers
pku2115 C Looooops
pku2142 the Balance
* Highly recommended:
sgu106 the equation
pku3708 Recurrent Function (classic)
5. Joseph Ring Question

This question is still more interesting, not difficult.
* Simple question:
pku3517 and then there is one
pku1781 in Danger
pku1012 Joseph
pku2244 Eeny Meeny Moo
Recommended
pku2886 who Gets the most candies?
6. Gaussian elimination method solution equation

The solution equation is not very difficult, that is, according to the method of linear algebra middle school, the coefficient matrix into the upper triangular matrix or the number matrix, but some questions to determine whether there is a solution, or enumerate all the solutions. But this kind of topic I think the more difficult or how to build this equation group, this understanding, there is no big problem.
* Simple title:
pku1222 EXTENDED LIGHTS out
pku1681 Painter ' s problem
pku1830 switch issues
* recommended:
pku2947 Widget Factory
pku2065 SETI
* strongly recommended:
pku1753 Flip Game
pku3185 The water bowls
* metamorphosis:
pku1487 single-player Games

7. Matrix
Solving the problem with matrices is very common, but I'm not using it very well, and I don't have a lot of problems. Suggest that you can go to see the Matrix67 of the 10 questions about the matrix, it is really classic, but not very good-looking understand.
* Simple:
pku3070 Fibonacci
pku3233 Matrix Power Series
pku3735 Training Little Cats
8. High-time congruence equation

I should have no say in this matter, A^b%c=d, I will only ask D and B now, alas, I would like to know how to ask for a. Just recommend a few questions, here involves a baby-step,giant-step algorithm.
pku3243 Clever Y
pku2417 Discrete Logging
9. Principle of tolerance, pigeon nest principle

Useful two theorems, but it seems that not many of these two theorems are tested separately.
* Pigeon Nest Principle:
pku2356 Find a multiple
pku3370 Halloween Treats
* Principle of repulsion:
hdu1695 GCD
hdu2461 rectangles
10. Find patterns and push formulas

This kind of topic design is generally very ingenious, it is really difficult to think out, but as long as the law or the introduction of formula, it is not very difficult. Many of me are in the context of other people's thinking, I can think of it is really not easy.
* Personal feeling is pretty good:
pku3372 Candy distribution
pku3244 Difference between triplets
pku1809 regetni
pku1831 indefinite equation set
pku1737 Connected Graph
pku2480 longge ' s problem
pku1792 Hexagonal Routes
11. Permutation combination, interval count, count sequence

These topics may require some combination of mathematical knowledge, basically high school knowledge is enough. Interval counting problems are generally not difficult, but when writing needs to be careful, all kinds of situations should be considered in place. As for the number of Cattleya, the difference sequence, Stirling number ... are also interesting, you can go to see "combinatorial mathematics."
* Simple title:
pku1850 Code
pku1150 the last Non-zero Digit
pku2282 The counting problem
pku3286 how many 0 ' s?
* recommended:
pku3252 Round Numbers
* count sequence:
pku1430 Binary Stirling Numbers
pku2515 Birthday Cake
pku1707 Sum of powers
12. Two Method

Two points of thought is still very important, here is a simple recommendation of a few purely two-part question.
Simple
pku3273 Monthly Expense
pku3258 River Hopscotch
pku1905 Expanding Rods
pku3122 Pie
Recommended
pku1845 Sumdiv
13. Stable marital problems

Inadvertently exposed to this algorithm, but also quite interesting, "combinatorial mathematics" in the detailed introduction.
pku3487 The Stable marriage problem
zoj1576 marriage is Stable
14. Digital Statistical problems

In the waypoint month race first contact This kind of question, Scau Daniel Little Dragon recommended I read a paper, 09 Liu Cong "Talking about the digital statistics problem", this paper is very wonderful, also quite detailed, each problem has detailed analysis and the author's reference code. So I have nothing to say, the code of these questions I do not post the blog, we go directly to the paper.
Simple:
ural1057 Amount of degrees
spoj1182 Sorted bit Squence
hdu3271 Snibb
More difficult:
spoj2319 Sequence
sgu390 Tickets

Poj number theory (RPM)

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