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A characterization of some q-multiplicative functions

Jean-Loup Mauclaire (2005)

Acta Arithmetica

A class of weakly perfect graphs

H. R. Maimani, M. R. Pournaki, S. Yassemi (2010)

Czechoslovak Mathematical Journal

A graph is called weakly perfect if its chromatic number equals its clique number. In this note a new class of weakly perfect graphs is presented and an explicit formula for the chromatic number of such graphs is given.

A convolution theorem with applications to some divisor functions.

A. Ivic (1978)

Publications de l'Institut Mathématique [Elektronische Ressource]

A formula for the number of solutions of a restricted linear congruence

K. Vishnu Namboothiri (2021)

Mathematica Bohemica

Consider the linear congruence equation $x_{1} + ... + x_{k} \equiv b (mod n^{s})$ for $b \in ℤ$ , $n, s \in ℕ$ . Let ${(a, b)}_{s}$ denote the generalized gcd of $a$ and $b$ which is the largest $l^{s}$ with $l \in ℕ$ dividing $a$ and $b$ simultaneously. Let $d_{1}, ..., d_{τ (n)}$ be all positive divisors of $n$ . For each $d_{j} ∣ n$ , define $𝒞_{j, s} (n) = {1 \leq x \leq n^{s} : {(x, n^{s})}_{s} = d_{j}^{s}}$ . K. Bibak et al. (2016) gave a formula using Ramanujan sums for the number of solutions of the above congruence equation with some gcd restrictions on $x_{i}$ . We generalize their result with generalized gcd restrictions on $x_{i}$ and prove that for the above linear congruence, the number of solutions...

A generalization of Menon's identity with respect to a set of polynomials.

Haukkanen, P., Wang, J. (1996)

Portugaliae Mathematica

A generalization of Pillai's arithmetical function involving regular convolutions

László Tóth (1998)

Acta Mathematica et Informatica Universitatis Ostraviensis

A generalization of the Smarandache function to several variables.

Hungerbühler, Norbert, Specker, Ernst (2006)

Integers

A generalization of the Subbarao identity.

Penntti Haukkanen (1988)

Aequationes mathematicae

A matrix inequality for Möbius functions.

Bordellès, Olivier, Cloitre, Benoit (2009)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

A Menon-type identity using Klee's function

Arya Chandran, Neha Elizabeth Thomas, K. Vishnu Namboothiri (2022)

Czechoslovak Mathematical Journal

Menon’s identity is a classical identity involving gcd sums and the Euler totient function $φ$ . A natural generalization of $φ$ is the Klee’s function $Φ_{s}$ . We derive a Menon-type identity using Klee’s function and a generalization of the gcd function. This identity generalizes an identity given by Y. Li and D. Kim (2017).