I have an absurdly simple algorithm which for N = 2^{2^{k-1}} +1 a composite Fermat Number, computes a divisor 1
The algorithm is also a test for primality, i.e. N is prime if and only if my algorithm has output e=N.
Features:
The algorithm is a k-step recursion. Hence it contains no steps which involve "Trial & Error".
The algorithm involves simple manipulations of bit strings. It uses non of the arithmetic operations +,-,*,/.
My goal is to prove that no such algorithm as I have just described is possible. This would be the contradiction in a theorem I proving.