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Notes on Number Theory and Discrete Mathematics Print
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