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2(n^2 +1)-n not a perfect square

Source: Czech-Polish-Slovak Junior Match 2012, Team p3 CPSJ

March 12, 2020
Perfect Squarenumber theory

Problem Statement

Prove that if nn is a positive integer then 2(n2+1)āˆ’n2 (n^2 + 1) - n is not a square of an integer.