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divisibility

Source: Ukraine 2005 grade 11

July 28, 2009
inductionnumber theory unsolvednumber theory

Problem Statement

Prove that for any integers n≥2 n \ge 2 there is a set An A_n of n n distinct positive integers such that for any two distinct elements i,j \in A_n, |i\minus{}j| divides i^2\plus{}j^2.
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