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Putnam 2000 A2

Source:

September 6, 2011
PutnamquadraticsalgebrapolynomialinductionDiophantine equationcollege contests

Problem Statement

Prove that there exist infinitely many integers nn such that nn, n+1n+1, n+2n+2 are each the sum of the squares of two integers. [Example: 0=02+020=0^2+0^2, 1=02+121=0^2+1^2, 2=12+122=1^2+1^2.]
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