乱数(LCGってやつ)なんですけど，ここ
http://en.wikipedia.org/wiki/Linear_congruential_generator
の，1-5の条件が言えれば周期がMになるそうですが，説明できるかたいますか?

以下，引用です．

LCGs are defined by the recurrence relation:

V_(j+1) = (A x V_j + B) mod M

Where Vn is the sequence of random values and A, B and M are generator-specific integer constants. mod is the modulo operation.

The period of a general LCG is at most M, and in most cases less than that. The LCG will have a full period if:

1. B and M are relatively prime
2. A-1 is divisible by all prime factors of M.
3. A-1 is a multiple of 4 if M is a multiple of 4
4. M > max(A, B, V0)
5. A > 0, B > 0