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(b^n-1)(b-1) is prime power then n is prime

Source: Estonia IMO TST 2007 p3

March 28, 2020
number theorypower of primeprime

Problem Statement

Let nn be a natural number, n>2n > 2. Prove that if bn−1b−1\frac{b^n-1}{b-1} is a prime power for some positive integer bb then nn is prime.
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