A variation of a congruence of Subbarao for n=2^(alpha)*5^(beta)

2016/07/05 by Bujačić, Sanda
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1607.01258

openalex publication_date 2016/07/05 · openalex created_date 2016/07/22 · openalex updated_date 2026/07/28

Abstract

There are many open problems concerning the characterization of the positive integers n fulfilling certain congruences and involving the Euler totient function φ and the sum of positive divisors function σ of the positive integer n. In this work, we deal with the congruence of the form nφ(n)≡2\pmodσ(n) and we prove that the only positive integers of the form 2^α5^β, \enspace α, β≥0, that satisfy the above congruence are n=1, 2, 5, 8.

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