Jacobi's two-square theorem states that the number of representations of a positive integer k as a sum of two squares, counting order and sign, is 4 times the surplus of positive divisors of k congruent to 1 modulo 4 over ...

In 1987 Knopfmacher and Knopfmacher published new infinite product expansions for real numbers 0 < A < 1 and A > 1. They called these expansions Engel product expansions. At that time they had difficulty finding rational ...

The Fibonacci identity belongs to a family of identities where each identity contains only one product on the right side. In this paper we give this family together with two other such families. We also state two conjectures ...

n this note, we give a necessary condition for the primality of (2p+1)/3.