MathDB

4

Part of 1988 Poland - Second Round

Problems(1)

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

Source: Polish MO Recond Round 1988 p4

9/9/2024
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 .
number theorydividesdivisible