A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
Identities for balancing numbers using generating function and some new congruence relations

2016
*
Notes on Number Theory and Discrete Mathematics Print
*
unpublished

It is well-known that the balancing numbers are the square roots of the triangular numbers and are the solutions of the Diophantine equation 1 + 2 +. .. + (n − 1) = (n + 1) + (n + 2) +. .. + (n + r), where r is the balancer corresponding to the balancing number n. Thus if n is a balancing number, then 8n 2 + 1 is a perfect square and its positive square root is called a Lucas-balancing number. The goal of this paper is to establish some new identities of these numbers.

fatcat:ghuuypt3qfd7rb25a55qg2ogeu