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Infinite subset of pairwise coprime integers

Source: Romanian TST 1997

September 17, 2011
number theory proposednumber theory

Problem Statement

Let a>1a>1 be a positive integer. Show that the set of integers {a2+a−1,a3+a2−1,…,an+1+an−1,…}\{a^2+a-1,a^3+a^2-1,\ldots ,a^{n+1}+a^n-1,\ldots\} contains an infinite subset of pairwise coprime integers.
Mircea Becheanu
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