Almost universal ternary sums of pentagonal numbers

2020/07/21 by Hai-Liang Wu, Li-Yuan Wang, Wu, Hai-Liang +1
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2007.10910

openalex publication_date 2020/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For each integer x, the x-th generalized pentagonal number is denoted by P₅(x)=(3x²-x)/2. Given odd positive integers a,b,c and non-negative integers r,s, we employ the theory of ternary quadratic forms to determine when the sum aP₅(x)+2^rbP₅(y)+2^scP₅(z) represents all but finitely many positive integers.

Citations

• Almost universal ternary sums of triangular numbers
• On x(ax+ 1)+y(by+ 1)+z(cz+ 1) and x(ax+b)+y(ay+c)+z(az+d)

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