The generalized form of Mersenne (x^n -1)/(x-1) can be generalized further to 
x^n - ((x-2)(x^k) +1)/(x-1) this formula computes x^n - (x^p - (x^(p-1) + 
x^(p-2) + x^(p-3) + . . .  + x ^2 + x + 1) ).  If n = p, x = 2, the result is 
a Mersenne.  You can go back farther and farther into this, but I think the 
three variable solution is the best of them.
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