I'm doing some homework and I need to answer why the increment (b) doesn't affect randomness in the mixed congruential method.
The formula is
$X_{n+1} \equiv (a X_n + b) \mod m$
I'm doing some homework and I need to answer why the increment (b) doesn't affect randomness in the mixed congruential method.
The formula is
$X_{n+1} \equiv (a X_n + b) \mod m$
Answer given by Robert Israel in the comments:
Assuming $\mathrm{gcd}\,(a−1,m)=1$, there is some $d$ such that $Y_n=X_n+d \mod m$ satisfies $Y_{n+1}=aY_n \mod m$, so all the increment accomplishes is a constant shift in the sequence.