Affiliation:
1. Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt
Abstract
Let
,
, and
be the balancing, Jacobsthal, and Lucas balancing numbers, respectively. In this paper, the diophantine equations
and
are completely solved. The solutions rely basically on Matveev’s theorem on linear forms in logarithms of algebraic numbers and a procedure of reducing the upper bound due to Dujella and Pethö.
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