Question

A linear congruential generator has a modulus of 32. How long can its cycle be?

Answer 1

Llinear congruential generator produce a sequence of integers between 0 and m−1 according to:

here a is the multiplier,c the increment and m the modulus

A linear congruential generator has full period (cycle length is m) if and only if the following conditions hold:

• The only positive integer that exactly divides both m and c is 1
• If q is a prime number that divides m, then q divides a−1
• If 4 divides m, then 4 divides a−1

Hence, if these condition satisfy, it can be 32