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A Remark on a Paper of Luca and Walsh
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Zhao-Jun Li
Published/Copyright:
August 4, 2011
Abstract
In 2002, F. Luca and P. G. Walsh studied the Diophantine equations of the form (ak – 1)(bk – 1) = x2, for all (a, b) in the range 2 ≤ b < a ≤ 100 with sixty-nine exceptions. In this paper, we solve two of the exceptions. In fact, we consider the equations of the form (ak – 1)(bk – 1) = x2, with (a, b) = (13, 4), (28, 13).
Keywords.: Diophantine Equation; Legendre Symbol
Received: 2010-07-05
Revised: 2011-03-27
Accepted: 2011-05-12
Published Online: 2011-08-04
Published in Print: 2011-December
© de Gruyter 2011
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Articles in the same Issue
- Completely Multiplicative Automatic Functions
- The k-Periodic Fibonacci Sequence and an Extended Binet's Formula
- Robin's Theorem, Primes, and a New Elementary Reformulation of the Riemann Hypothesis
- Reducing the Erdős–Moser Equation 1n + 2n + ⋯ + kn = (k + 1)n Modulo k and k2
- On Some Conjectures Concerning Stern's Sequence and Its Twist
- Number of Weighted Subsequence Sums with Weights in {1, –1}
- Binomial Coefficient – Harmonic Sum Identities Associated to Supercongruences
- Euler's Pentagonal Number Theorem Implies the Jacobi Triple Product Identity
- On Directions Determined by Subsets of Vector Spaces over Finite Fields
- A Remark on a Paper of Luca and Walsh
- On the Tennis Ball Problem
- On the Conditioned Binomial Coefficients
- Convolution and Reciprocity Formulas for Bernoulli Polynomials
- Counting Finite Languages by Total Word Length
