Hello! This is a nice problem from Putnam a few years ago, for fun.

Show that there are infinitely many triples of consecutive integers, each of which is the sum of two squares.

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- December 4th 2009, 12:10 AMBruno J.Sums of squares : putnam problem
Hello! This is a nice problem from Putnam a few years ago, for fun.

Show that there are infinitely many triples of consecutive integers, each of which is the sum of two squares. - December 4th 2009, 12:40 AMNonCommAlg
- December 4th 2009, 12:46 AMBruno J.
Very nice! Your intuition is very good.

My solution is different. I show that given any triple , you can construct another triple. Since sums of two squares are closed under product, is a sum of two squares, and thus we obtain . So it suffices to show that we have one such triple, and 8,9,10 does the job.

Yours is better though (Happy) - December 4th 2009, 12:55 AMNonCommAlg