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The American Mathematical Monthly Volume 117, 2010 - Issue 7
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Notes

The Diophantine Equation x4 ± y4 = iz2 in Gaussian Integers

Filip NajmanDepartment of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, [email protected]
Pages 637-641 | Published online: 13 Dec 2017
 
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Abstract

In this note we find all the solutions of the Diophantine equation x4 ± y4 = iz2 using elliptic curves over ℚ(i). Also, using the same method we give a new proof of Hilbert's result that the equation x4 ± y4 = z2 has only trivial solutions in Gaussian integers.

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