gcd(xa - 1 , xb - 1) = xgcd(a , b) - 1 (x>1,a,b>0) （HDU 2685）
gcd (fib [m], fib [n]) = fib [gcd (m, n)] fib Fibonacci number is
gcd(fib[ m ] , fib[ n ]) = fib[ gcd(m , n) ]
lcm (a, kb) = k * lcm (a, b)
lcm(a/b , c/d) = lcm(a , c) / gcd(b , d)
a > b , gcd(a , b)==1 , 则gcd(am - bm , an - bn) = agcd(m , n) - bgcd(m , n)
= GCD set G (C . 1 n- , C 2 n- , ········· C n- n- ) of G is: (HDU2582)
- n is a prime number: se
- a plurality of prime factor n: 1
- n prime factors only: the factor
Euler function of all of the factors of a number equal to the number itself
The maximum edge weights minimum spanning tree is a maximum spanning all minimum edge weight (MST minimum spanning tree on the right side of all the maximum)
Wilson's Theorem: p is a prime number is equivalent to (p -1) ≡ -1 (mod p) i.e. p | (p-1) + 1 (HDU 6608)!!
Fermat's little theorem: If p is a prime number, and a is not an integer multiple of p, there is a (p-. 1) ≡1 (MOD p)
Fermat - Euler's theorem: If n, a is a positive integer, and n, a prime, then: 
Hall theorem: determining necessary and sufficient condition is bipartite graph matching perfectly: first requirement | X | == | Y | (approximately equal number of points) , for any subset of X has a | a | <= | b | , wherein b is a set of points can be achieved and
Hall Theorem Corollary: For bipartite graph G = {X + Y, E}, the maximum matching M = | X | - max (| S | - | N (S) |) subset (S X with, N (S ) can reach the point S is set and) (| S | may be 0, so the latter must not less than 0) (HDU6667)
If p% 4 = 3, x ^ 2 = a (mod p) then x = ± pow (a, (p + 1) / 4, p)
(a + b) p ≡ ap + bp (mod p)
If a * bc * d == 1, then a and c, a and d, b and c, b and d are coprime