The Parametric Representation for Diophantine Equation x2 + y2 + z2 = t2 of Polygonal Numbers

Abstract. The paper Pythagorean triples of Polygonal Numbers [3] called our attention to search on another parametric representation for Diophantine equation of x2+y2+z2 = t2 of n-polygonal numbers. We got benefit from the identity that gives all the solutions of the equation x2+ y2+ z2 = t2 in natural numbers. It is the aim of this paper to give the most anologous parametric representation for Diophantine equation of x2 + y2 + z2 = t2 of n-polygonal numbers. The proof is given in a computational aspect