**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)

pku2409 Let It bead

pku2154 Color

pku1286 Necklace of Beads

* 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

pku1715 hexadecimal Numbers

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)