A note on distinct integer triplets summing to a perfect square in pairs

By Soubhik Chakraborty.

Abstract: Let i, j and k be three distinct positive integers (we call it a triplet)such that the sum of every pair in the triplet is a perfect square. For example, (2, 34, 47) is a permissible triplet. Permuting the elements of a triplet among themselves, we get six triplets for each combination. The note raises the non trivial problem of finding a functional relationship between c and n where c is the number of such combination triplets such that i, j, k <=n where n is a positive integer.

Key Words: combination triplets; perfect square

Soubhik Chakraborty, soubhikc@yahoo.co.in

Editor: Richard G. Graf, rgraf@sunstroke.sdsu.edu

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