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On the Diophantine equation z2 = x4 + Dx2y2 + y4

Published online by Cambridge University Press:  18 May 2009

J. H. E. Cohn
J. H. E. Cohn
Affiliation:
Department of Mathematics, Royal Holloway University of London, Egham, Surrey, TW20 0EX, England
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The equation of the title in positive integers x, y, z where D is a given integer has been considered for some 300 years [4, pp 634–639]. As observed by V. A. Lebesgue, and probably known to Euler, if x, y, z is one non-trivial solution i.e., one with xy(x2 – y2) ≠0, another is given by . It then follows that there are infinitely many such with (x, y) = 1. The question that remains is to determine for which values of D such solutions exist.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 3 , September 1994 , pp. 283 - 285
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

REFERENCES

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