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The parametric representation for Diophantine equation x^2+y^2+z^2=t^2 of polygonal numbers

2007
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International Mathematical Forum
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The paper Pythagorean triples of Polygonal Numbers [3] called our attention to search on another parametric representation for Diophantine equation of x 2 + y 2 + z 2 = t 2 of n-polygonal numbers. We got benefit from the identity that gives all the solutions of the equation x 2 + y 2 + z 2 = t 2 in natural numbers. It is the aim of this paper to give the most anologous parametric representation for Diophantine equation of x 2 + y 2 + z 2 = t 2 of n-polygonal numbers. The proof is given in a computational aspect.

doi:10.12988/imf.2007.07262
fatcat:cz7r5as4hzho5gl3sf6cg27o5u