Some New Properties of Balancing Numbers and Square Triangular Numbers

Abstract

A number N is a square if it can be written as N = n 2 for some natural number n; it is a triangular number if it can be written as N = n(n + 1)/2 for some natural number n; and it is a balancing number if 8N 2 +1 is a square. In this paper, we study some properties of balancing numbers and square triangular numbers. 1