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x is a non-integer rational number, x^n+(x+1)^n is an integer

Source: 2021 Turkey JBMO TST P2

May 23, 2021
number theory solvedTurkey

Problem Statement

For which positive integers nn, one can find a non-integer rational number xx such that xn+(x+1)nx^n+(x+1)^n is an integer?
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