Article

Integer partitions into Diophantine pairs

Published in: Quaestiones Mathematicae
Volume 40 , issue 4 , 2017 , pages: 435–442

DOI: 10.2989/16073606.2017.1296903

Author(s): F. Bencherif USTHB University, Algeria , N. Benyahia-Tani Algiers 3 University, Algeria , S. Bouroubi USTHB University, Algeria , O. Kihel Brock University, Canada , Z. Yahi Abderahmane Mira University, Algeria

Keywords: Primary 05A17 , Secondary 11P83 , Primary 05A17 , Secondary 11P83

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Abstract

Let n, a and b be positive integers. The pair (a, b) is called an integer partition of n into Diophantine pair if n = a + b, ab + 1 is a perfect square and a > b. In this paper we give, for any positive integer n, a closed formula for the number of integer partitions into Diophantine pairs.

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