On the congruence $2\sp {n-k}\equiv 1\;({\rm mod}\,n)$

NOTES ON CONGRUENCE n-PERMUTABILITY AND SEMIDISTRIBUTIVITY

In [1] T. Dent, K. Kearnes and Á. Szendrei define the derivative, Σ′, of a set of equations Σ and show, for idempotent Σ, that Σ implies congruence modularity if Σ′ is inconsistent (Σ′ |= x ≈ y). In this paper we investigate other types of derivatives that give similar results for congruence n-permutable for some n, and for congruence semidistributivity. In a recent paper [1] T. Dent, K. Kearne...

On Congruence Properties of Consecutive Values of P(n,m)

In the late 19th century, Sylvester and Cayley investigated the properties of the partition function p(n, m). This function enumerates the partitions of a non-negative integer n into exactly m parts. The author here extends techniques developed in a previous publication to investigate the congruence properties of consecutive values of the function p(n, m).

ON THE CONGRUENCE ax

We give bounds on the number of solutions to the Diophantine equation (X +1/x)(Y +1/y) = n as n tends to infinity. These bounds are related to the number of solutions to congruences of the form ax + by ≡ 1 modulo xy.

Equations implying congruence n-permutability and semidistributivity

T. Dent, K. Kearnes and Á. Szendrei have defined the derivative, Σ′, of a set of equations Σ and shown, for idempotent Σ, that Σ implies congruence modularity if Σ′ is inconsistent (Σ′ |= x ≈ y). In this paper we investigate other types of derivatives that give similar results for congruence n-permutability for some n, and for congruence semidistributivity.

RAMANUJAN'S FUNCTION r{n)—k CONGRUENCE PROPERTY