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A specially multiplicative arithmetic function is the Dirichlet convolution of two completely multiplicative arithmetic functions. The aim of this paper is to prove explicitly that two mathematical objects, namely $(a, b)$ -Fibonacci sequences and specially multiplicative prime-independent arithmetic functions, are equivalent in the sense that each can be reconstructed from the other. Replacing one with another, the exploration space of both mathematical objects expands significantly.

A note on a paper by Brenner.

Tzermias, Pavlos (2002)

International Journal of Mathematics and Mathematical Sciences

A note on character sums over finite fields.

D.A. Burgess (1972)

Journal für die reine und angewandte Mathematik

A note on Deaconescu's result concerning Lehmer's problem.

Hernández Hernández, Santos, Luca, Florian (2008)

Integers

A note on factorization of the Fermat numbers and their factors of the form $3 h 2^{n} + 1$

Michal Křížek, Jan Chleboun (1994)

Mathematica Bohemica

We show that any factorization of any composite Fermat number $F_{m} = {2^{2}}^{m} + 1$ into two nontrivial factors can be expressed in the form $F_{m} = (k 2^{n} + 1) (ℓ 2^{n} + 1)$ for some odd $k$ and $ℓ, k \geq 3, ℓ \geq 3$ , and integer $n \geq m + 2, 3 n < 2^{m}$ . We prove that the greatest common divisor of $k$ and $ℓ$ is 1, $k + ℓ \equiv 0 m o d 2^{n}, m a x (k, ℓ) \geq F_{m - 2}$ , and either $3 | k$ or $3 | ℓ$ , i.e., $3 h 2^{m + 2} + 1 | F_{m}$ for an integer $h \geq 1$ . Factorizations of $F_{m}$ into more than two factors are investigated as well. In particular, we prove that if $F_{m} = {(k 2^{n} + 1)}^{2} (ℓ 2^{j} + 1)$ then $j = n + 1, 3 | ℓ$ and $5 | ℓ$ .

A Note on Formulae for the nth Prime.

K.S. Subramonian-Namboodiripad (1971)

Monatshefte für Mathematik

A note on generalized mobius ...-functions

G. Victor Albis (1968)

Revista colombiana de matematicas

A note on linear recurrent Mahler numbers.

Barat, Guy, Frougny, Christiane, Pethő, Attila (2005)

Integers

A note on multiplicatively e-perfect numbers.

Le Anh Vinh, Dang Phuong Dung (2006)

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

A note on perfect totient numbers.

Deng, Moujie (2009)

Journal of Integer Sequences [electronic only]

A Note on prime k-th power nonresidues.

Richard H. Hudson (1983)

Manuscripta mathematica

A note on primes p with $σ (p^{m}) = z^{n}$

Maohua Le (1991)

Colloquium Mathematicae

A note on pseudoprimes with respect to abelian linear recurring sequence

František Marko (1996)

Mathematica Slovaca

A note on rational surgeries on a Hopf link

Velibor Bojković, Jovana Nikolić, Mladen Zekić (2023)

Czechoslovak Mathematical Journal

It is clear that every rational surgery on a Hopf link in $3$ -sphere is a lens space surgery. In this note we give an explicit computation which lens space is a resulting manifold. The main tool we use is the calculus of continued fractions. As a corollary, we recover the (well-known) result on the criterion for when rational surgery on a Hopf link gives the $3$ -sphere.

A note on recurrent mod p sequences

Umberto Zannier (1982)

Acta Arithmetica

A note on Sándor type functions.

Anitha, N. (2005)

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

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