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TOT 069 1984 Autumn Train J3 solve 2^n + 7 = x^2 in Z and in R

Source:

August 24, 2019
algebranumber theoryDiophantine equationdiophantineequation

Problem Statement

Find all solutions of 2n+7=x22^n + 7 = x^2 in which n and x are both integers . Prove that there are no other solutions.