Sums of two squares and a power

Rainer Dietmann, Christian Elsholtz

Research output: Chapter in Book/Report/Conference proceedingOther contribution


We extend results of Jagy and Kaplansky and the present authors and show that for all k ≥ 3 there are infinitely many positive integers n, which cannot be written as x2 + y2 + zk = n for positive integers x, y, z, where for k≢0mod4k≢0mod4 a congruence condition is imposed on z. These examples are of interest as there is no congruence obstruction itself for the representation of these n. This way we provide a new family of counterexamples to the Hasse principle or strong approximation.
Original languageEnglish
Title of host publicationFrom arithmetic to zeta-functions
PublisherSpringer, [Cham]
Number of pages6
Publication statusPublished - 31 Dec 2016

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