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(n-1)^2 \ n^{n-1}-1 for n > 2

Source: Mexican Mathematical Olympiad 1990 OMM P3

July 29, 2018
number theoryexponential

Problem Statement

Show that nn−1−1n^{n-1}-1 is divisible by(n−1)2 (n-1)^2 for n>2n > 2.
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