Functiones et Approximatio Commentarii Mathematici

Sums of two squares and one biquadrate

Rainer Dietmann and Christian Elsholtz

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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.

Article information

Source
Funct. Approx. Comment. Math., Volume 38, Number 2 (2008), 233-234.

Dates
First available in Project Euclid: 19 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.facm/1229696542

Mathematical Reviews number (MathSciNet)
MR2492913

Zentralblatt MATH identifier
1207.11046

Subjects
Primary: 11E25: Sums of squares and representations by other particular quadratic forms
Secondary: 11P05: Waring's problem and variants

Keywords
Sums of squares Waring's problem for mixed powers

Citation

Dietmann, Rainer; Elsholtz, Christian. Sums of two squares and one biquadrate. Funct. Approx. Comment. Math. 38 (2008), no. 2, 233--234. https://projecteuclid.org/euclid.facm/1229696542


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References

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  • Jagy, W.C. & Kaplansky, I. Sums of squares, cubes, and higher powers, Experiment. Math. 4 (1995), no. 3, 169--173.