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On D. J. Lewis's Equation x3+117y3 = 5

Published online by Cambridge University Press:  20 November 2018

R. Finkelstein  and
H. London
R. Finkelstein
Affiliation:
Bowling Green State University, Bowling Green, Ohio
H. London
Affiliation:
McGill University, Montreal, Quebec
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In a recent publication [2], D. J. Lewis stated that the Diophantine equation x3+117y3 = 5 has at most 18 integer solutions, but the exact number is unknown. In this paper we shall solve this problem by proving the following

Theorem. The equationx3+117y3 = 5 has no integer solutions.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 111
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Delone, B. N. and Faddeev, D. K., The theory of irrationalities of the third degree, Amer. Math. Soc, Providence, R.I., 1964.Google Scholar
2. LeVeque, W. J., Studies in number theory, Math. Assoc, of America, Washington, D.C., 1969.Google Scholar
3. Selmer, E. S., The Diophantine Equation ax3+ by3 + cz3 =0, Acta Math. 85 (1951), 203-362.Google Scholar