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A subset- Iran 3rd round-Number Theory 2007

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July 28, 2010
number theory unsolvednumber theory

Problem Statement

Let a>1a >1 be a positive integer. Prove that the set {a2+a−1,a3+a−1,⋯ }\{a^2+a-1,a^3+a-1,\cdots\} have a subset SS with infinite members and for any two members of SS like x,yx,y we have gcd⁡(x,y)=1\gcd(x,y)=1. Then prove that the set of primes has infinite members.
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