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

Volume: 86, Issue: 2, Pages: 348 - 352
Published: Oct 1, 2012
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:...
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Title
On the Diophantine equation $(8n)^{x}+(15n)^{y}=(17n)^{z}$
Published Date
Oct 1, 2012
Volume
86
Issue
2
Pages
348 - 352
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