On t-Balancers, t-Balancing Numbers and Lucas t-Balancing Numbers

Abstract

In this work, we determined the general terms of $t-$balancers, $t-$balancing numbers and Lucas $t-$balancing numbers by solving the Pell equation $2x^{2}-y^{2}=2t^{2}+4t+1$ for some integer $t\geq 1.$}