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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 +y +z = t of n-polygonal numbers. We got benefit from the identity that gives all the solutions of the equation x + y + z = t in natural numbers. It is the aim of this paper to give the most anologous parametric representation for Diophantine equation of x + y + z = t of n-polygonal numbers. The proof is given in a computational aspect. Mathematics Subject Classification: Primary 11D09, 11D72; Secondary 11Y16

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