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If (b^{n}-1)(b-1) is perfect square then 8 divides b

Source: Federation of Bosnia, 1. Grades 2008.

April 23, 2008
modular arithmetic

Problem Statement

Let b b be an even positive integer. Assume that there exist integer n>1 n > 1 such that \frac {b^{n} \minus{} 1}{b \minus{} 1} is perfect square. Prove that b b is divisible by 8.
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