# On the Diophantine equation (8n)^{x}+(15n)^{y}=(17n)^{z}

Published on Oct 1, 2012in Bulletin of The Australian Mathematical Society0.63

Â· DOI :10.1017/S000497271100342X

Abstract

Let a,b,cbe relatively prime positive integers such that a^{2}+b^{2}=c^{2}.In 1956, Je\'{s}manowicz conjectured that for any given positive integer nthe only solution of (an)^{x}+(bn)^{y}=(cn)^{z}in positive integers is (x,y,z)=(2,2,2) In this paper, we show that (8n)^{x}+(15n)^{y}=(17n)^{z}has no solution other than (x,y,z)=(2,2,2)in positive integers.
DOI: 10.1017/S000497271100342X