Some remarks on regular integers modulo n

A Gcd-Sum Function Over Regular Integers Modulo n

We introduce a gcd-sum function involving regular integers (mod n) and prove results giving its minimal order, maximal order and average order.

Extremal orders of some functions connected to regular integers modulo n

Let V (n) denote the number of positive regular integers (mod n) less than or equal to n. We give extremal orders of V (n)σ(n) n2 , V (n)ψ(n) n2 , σ(n) V (n) , ψ(n) V (n) , where σ(n), ψ(n) are the sum-of-divisors function and the Dedekind function, respectively. We also give extremal orders for σ∗(n) V (n) and φ∗(n) V (n) , where σ∗(n) and φ∗(n) represent the sum of the unitary divisors of n a...

Some Remarks on Regular Words

Some Remarks on Prime Factors of Integers

O ct 2 00 7 Regular integers modulo n László Tóth ( Pécs , Hungary ) October

Let n = p ν 1 1 · · · p νr r > 1 be an integer. An integer a is called regular (mod n) if there is an integer x such that a 2 x ≡ a (mod n). Let ̺(n) denote the number of regular integers a (mod n) such that 1 ≤ a ≤ n. Here ̺(n) = (φ(p ν 1 1) + 1) · · · (φ(p νr r) + 1), where φ(n) is the Euler function. In this paper we first summarize some basic properties of regular integers (mod n). Then in or...