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(x + 2)^n - x^n = 1 + 7^n diophantine

Source: Singapore Open Math Olympiad 1996 2nd Round p3 SMO

April 2, 2020
number theoryDiophantine equationdiophantine

Problem Statement

Let nn be a positive integer. Prove that there is no positive integer solution to thxe equation (x+2)nāˆ’xn=1+7n(x + 2)^n - x^n = 1 + 7^n.
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