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.
Citation
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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