6-3 For Oversea Coverage

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On the Diophantine Equation x^6+ky^3=z^6+kw^3

Given the positive integers m,n, solving the well known symmetric Diophantine equation xm+kyn=zm+kwn, where k is a rational number, is a challenge. By computer calculations, we show that for all integers k from 1 to 500, the Diophantine equation x6+ky3=z6+kw3 has infinitely many nontrivial (y≠w) rational solutions. Clearly, the same result holds for positive integers k whose cube-free part is n...

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ژورنال

عنوان ژورنال: The Journal of the Institute of Television Engineers of Japan

سال: 1977

ISSN: 1884-9644

DOI: 10.3169/itej1954.31.10_811