5 papers
An identity for the odd double factorial
Saud Hussein
The ordinary factorial may be written in terms of the Stirling numbers of the second kind as shown by Quaintance and Gould and the odd double factorial in terms of the Stirling num…
Wilson's and Wolstenholme's Theorems
Saud Hussein
We provide a proof of Wilson's Theorem and Wolstenholme's Theorem based on a direct approach by Lagrange requiring only basic properties of the primes and the Binomial theorem. The…
An Identity for the Partition Function Involving Parts of k Different Magnitudes
Saud Hussein
Using previous work by Merca, we show the partition function involving parts of k different magnitudes, shifted by the triangular numbers, equals the self convolution of the unrest…
A note on the converse of Wolstenholme's Theorem
Saud Hussein
Given a prime p and a positive integer m satisfying a certain inequality, the converse of Wolstenholme's Theorem is shown to hold for the product mp^k where k is any positive integ…
New conjecture related to a conjecture of McIntosh
Saud Hussein
We introduce a new conjecture on products of two distinct primes that would provide a partial answer to a conjecture of McIntosh. Also, is written in terms of…