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n^{2n} - n^{n+2} + n^n - 1 is divisible by (n - 1 )^3

Source: Polish MO Recond Round 1988 p4

September 9, 2024
number theorydividesdivisible

Problem Statement

Prove that for every natural number n n , the number n2n−nn+2+nn−1 n^{2n} - n^{n+2} + n^n - 1 is divisible by (n−1)3 (n - 1 )^3 .
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