Hardy-Ramanujan Journal |

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.

Source : oai:HAL:hal-01986713v1

Published on: January 23, 2019

Accepted 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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