What is the period of N xored identical random number generators, with differing seeds?
I will assume the N random generators have independent seeds and states.  Suppose their periods are $t_1,\dots,t_N$.  Then the period of their xor is a divisor of $\operatorname{lcm}(t_1,\dots,t_N)$.  Typically, it will be exactly $\operatorname{lcm}(t_1,\dots,t_N)$, but I don't know whether that is guaranteed in all cases.

If all $N$ generators have the same period $t$, then the period of their xor is a divisor of $t$ (and thus cannot be any larger than $t$).