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Find all n for which the coefficients are all divisible by 7

Source: Turkey National Olympiad 2006 - D1 - P3

January 6, 2007
algebrapolynomialnumber theory unsolvednumber theory

Problem Statement

Find all positive integers nn for which all coefficients of polynomial P(x)P(x) are divisible by 7,7, where P(x)=(x2+x+1)n−(x2+1)n−(x+1)n−(x2+x)n+x2n+xn+1.P(x) = (x^2 + x + 1)^n - (x^2 + 1)^n - (x + 1)^n - (x^2 + x)^n + x^{2n} + x^n + 1.
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