The Diophantine equations x1n + x2n + . . . + xrn1 = y1n + y2n + . . . + yrn2

Abstract

The aim of this paper is to prove the possibility of linearization of such equations by means of introduction of new variables. For n = 2 such a procedure is well known, when new variables are components of spinors and they are widely used in mathematical physics. For example, parametrization of Pythagoras threes a2 + b2 , a2 − b2 , 2ab may be cited as an example in number theory where two independent variables form a spinor which can be obtained by solution of a system of two linear equations.