6 days to 2016 Crazy Polynomials

Algebra Level 5

Find the number of ordered pairs ( P ( x ) , Q ( x ) ) (P(x),Q(x)) of polynomials with integer coefficients such that

( P ( x ) ) 2 + ( Q ( x ) ) 2 = ( x 4096 − 1 ) 2 . \large{ (P(x))^{2}+(Q(x))^{2}=(x^{4096}-1)^{2} }.


The answer is 708588.

Department 8 by Department 8 , 27, Israel

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