A Sufficient Condition for a Certain Set of Positive Integers to be Subset-Sum-Distinct

Let S be a set of positive integers.We say that S is a subset-sum-distinct set (briefly, S is an SSD-set) if for any two finite subsets X, Y of S,For fixed positive integers n and p, we set S(n, p) := {1 p , 2 p , 3 p , . . ., n p }.We prove a sufficient condition for which S(n, p) is an SSD-set.

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Published
2025-01-01
DOI
https://doi.org/10.33790/cpam1100116
Primary Topic
Analytic Number Theory Research
Type
article
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article

A Sufficient Condition for a Certain Set of Positive Integers to be Subset-Sum-Distinct

Yasuhiko Kamiyama
Analytic Number Theory Research
article

A Sufficient Condition for a Certain Set of Positive Integers to be Subset-Sum-Distinct

Yasuhiko Kamiyama
article en

Abstract

Let S be a set of positive integers.We say that S is a subset-sum-distinct set (briefly, S is an SSD-set) if for any two finite subsets X, Y of S,For fixed positive integers n and p, we set S(n, p) := {1 p , 2 p , 3 p , . . ., n p }.We prove a sufficient condition for which S(n, p) is an SSD-set.

Vol. 3(1)
University of the Ryukyus (JP)
Openalex Percentile: Top 75%
Analytic Number Theory Research
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A Sufficient Condition for a Certain Set of Positive Integers to be Subset-Sum-Distinct — Yasuhiko Kamiyama · (2025) | TGRS Research Map | TGRS