t-balancing numbers, Pell numbers and square triangular numbers

Tekcan, Ahmet and Yazla, Aziz (2017) t-balancing numbers, Pell numbers and square triangular numbers. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 33 (2). pp. 133-146. ISSN 0866-0174

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Abstract

Let t ≥ 2 be an integer. In this work we get all integer solutions of the Diophantine equation 8r 2 + 8tr + 1 = y 2 in order to determine the general terms of all t−balancing numbers for which 2t 2 − 1 is prime. Later we obtain some formulas for the sums of Pell, Pell–Lucas, balancing and Lucas–balancing numbers in terms of t−balancing numbers and also we deduce the general terms of all t−balancing numbers in terms of square triangular numbers.

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