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Metaconjugation and Quadratic Forms

Adriana Cardoso, António Leite, António Machiavelo, Rafael Moreira, Luís Roçadas

math.NTarXiv:2608.24854

Abstract

We present a quaternionic proof that the quadratic form t2+2x2+5y2+10z2 represents all positive integers, and that the form t2+x2+7y2+7z2 represents all natural numbers which are neither equal to 3 · 7 nor equal to 6 · 7, for any ∈ N0. To do this we introduce a technique that may be useful for other purposes, and that we call "metaconjugation".

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