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Displaying 21 – 40 of 1807

A continued fraction of order twelve

M. Mahadeva Naika, B. Dharmendra, K. Shivashankara (2008)

Open Mathematics

In this paper, we establish several explicit evaluations, reciprocity theorems and integral representations for a continued fraction of order twelve which are analogues to Rogers-Ramanujan’s continued fraction and Ramanujan’s cubic continued fraction.

A convolution theorem with applications to some divisor functions.

A. Ivic (1978)

Publications de l'Institut Mathématique [Elektronische Ressource]

A criterion for periodicity of multi-continued fraction expansion of multi-formal Laurent series

Zongduo Dai, Ping Wang, Kunpeng Wang, Xiutao Feng (2007)

Acta Arithmetica

A decision method for the recognizability of sets defined by number systems

Juha Honkala (1986)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

A density result for elliptic Dedekind sums

Hiroshi Ito (2004)

Acta Arithmetica

A Diophantine property associated with prime twins.

Shiu, P. (2005)

Experimental Mathematics

A divisibility property of binomial coefficients viewed as an elementary sieve.

Hudson, Richard H., Williams, Kenneth S. (1981)

International Journal of Mathematics and Mathematical Sciences

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...