On Certain Quaternary Quadratic Forms

2014/11/14 by Kazuhide Matsuda, Matsuda, Kazuhide · 1 citation
Mathematics · #11E25 #14K25 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1411.6963

openalex publication_date 2014/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we determine all the positive integers a, b and c such that every nonnegative integer can be represented as f^a,b_c(x,y,z,w)=ax²+by²+c(z²+zw+w²) \textrmwith x,y,z,w∈ℤ. Furthermore, we prove that f^a,b_c can represent all the nonnegative integers if it represents n=1,2,3,5,6,10.

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