Hey there I'm looking for the proof of Knuth's Theorem such that it satisfies its following formulation:
The linear congruential generator $h(x) = (ax + c) \mod k$ has cycle length $k$, if and only if
(1) $c$ are $k$ relatively prime
(2) every prime factor of $k$ divides $a − 1$
(3) if $4$ divides $k$, then $4$ divides $a − 1$