Sums of two squares and one biquadrate

Rainer Dietmann; Christian Elsholtz

doi:10.7169/facm/1229696542

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Home > Journals > Funct. Approx. Comment. Math. > Volume 38 > Issue 2 > Article

September 2008 Sums of two squares and one biquadrate

Rainer Dietmann, Christian Elsholtz

Funct. Approx. Comment. Math. 38(2): 233-234 (September 2008). DOI: 10.7169/facm/1229696542

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Abstract

There are no nontrivial integer solutions of $x^2+y^2+z^4=p^2$ for primes $p \equiv 7 \pmod 8$, even though there are no congruence obstructions.

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Rainer Dietmann. Christian Elsholtz. "Sums of two squares and one biquadrate." Funct. Approx. Comment. Math. 38 (2) 233 - 234, September 2008. https://doi.org/10.7169/facm/1229696542

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Published: September 2008

First available in Project Euclid: 19 December 2008

zbMATH: 1207.11046

MathSciNet: MR2492913

Digital Object Identifier: 10.7169/facm/1229696542

Subjects:

Primary: 11E25

Secondary: 11P05

Keywords: sums of squares , Waring's problem for mixed powers

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Funct. Approx. Comment. Math.

Vol.38 • No. 2 • September 2008

Adam Mickiewicz University, Faculty of Mathematics and Computer Science

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Rainer Dietmann, Christian Elsholtz "Sums of two squares and one biquadrate," Functiones et Approximatio Commentarii Mathematici, Funct. Approx. Comment. Math. 38(2), 233-234, (September 2008)

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