Number Theory

    

Power Spectral Pythagorean Numbers

Authors: Walter A. Kehowski

A power spectral number is a positive integer whose spectral basis consists of only primes and powers. If one searches for power spectral numbers whose spectral sum is also a power, then one finds only five examples. We call these numbers power spectral Pythagorean numbers. The first two examples involve the Pythagorean triples 3,4,5 and 8,15,17. It is shown in this note that these are the only two Pythagorean triples that are power spectral Pythagorean. The other three examples involve the Pell equation.

Comments: 11 Pages. Some improvements in the presentation as well as a new section with an impossibility result.

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Submission history

[v1] 2026-01-27 01:58:49
[v2] 2026-03-10 23:58:09

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