József Sándor - A note on some congruences involving arithmetic functions

hrj:5115 - Hardy-Ramanujan Journal, January 23, 2019 - https://doi.org/10.46298/hrj.2019.5115
A note on some congruences involving arithmetic functions

Authors: József Sándor

We consider some congruences involving arithmetical functions. For example, we study the congruences nψ(n) ≡ 2 (mod ϕ(n)), nϕ(n) ≡ 2 (mod ψ(n)), ψ(n)d(n) − 2 ≡ 0 (mod n), where ϕ(n), ψ(n), d(n) denote Euler's totient, Dedekind's function, and the number of divisors of n, respectively. Two duals of the Lehmer congruence n − 1 ≡ 0 (mod ϕ(n)) are also considered.

Published on: January 23, 2019
Submitted on: January 23, 2019
Keywords: Euler's totient,Dedekind's arithmetical function,number of divisors,primality,congruences 2010 Mathematics Subject Classification 11A25,11A07,11D45,11N05, [ MATH ] Mathematics [math], [ MATH.MATH-NT ] Mathematics [math]/Number Theory [math.NT]


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