Supercobalancing Numbers

Abstract

A natural number n is called cobalancing number (with cobalancer r) if it satisfies the Diophantine equation 1+2+·· ·+n = (n+1)+(n+2)+·· ·+(n+r). However, if for some pair of natural numbers (n, r), 1+2+· · ·+n > (n+1)+(n+2)+· · ·+(n+r) and equality is achieved after adding a natural number D to the right hand side then we call n a D-supercobalancing number with D-supercobalaner number r. In this paper, such numbers are studied for certain values of D.