New examples of the representation of 1 by the sum of reciprocals of semiprime numbers

2020/09/01 by Tatsuru Watanabe, Watanabe, Tatsuru
Computer Science · Mathematics · #11D68 #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2009.03275

openalex publication_date 2020/09/01 · openalex created_date 2020/09/11 · openalex updated_date 2026/07/28

Abstract

In 1978, Allan.Wm.Johnson obtained an example of the representation of 1 by the sum of reciprocals of the product of two distinct prime numbers. His example has 48 terms [1], and we had no examples which have less than 48 terms until now. In this paper, we construct 17 new examples that have less than 48 terms. Since all of the new examples have 47 terms and we have no examples which have less than 47 terms, it is assumed that the minimum number of terms is 47.

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