Multiple reciprocal sums and multiple reciprocal star sums of polynomials are almost never integers

2017/03/21 by Shaofang Hong, Liping Yang, Hong, Shaofang +5
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1703.07263

openalex publication_date 2017/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let n and k be integers such that 1≤ k≤ n and f(x) be a nonzero polynomial of integer coefficients such that f(m)≠ 0 for any positive integer m. For any k-tuple s=(s₁, ..., s_k) of positive integers, we define H_k,f(s, n):=∑_1≤ i₁

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