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  • ON THE DIOPHANTINE EQUATION (8n)x+(15n)y=(17n)z

  • Part of
  • ZHI-JUAN YANG, MIN TANG
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 86 / Issue 2 / October 2012
    Published online by Cambridge University Press:
    07 February 2012, pp. 348-352
    Print publication:
    October 2012
    • Article
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  • Let a,b,c be relatively prime positive integers such that a2+b2=c2. Half a century ago, Jeśmanowicz [‘Several remarks on Pythagorean numbers’, Wiadom. Mat.1 (1955/56), 196–202] conjectured that for any given positive integer n the 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 in positive integers other than (x,y,z)=(2,2,2).