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Your search keyword '"Walsh, P. G."' showing total 9 results
Start Over Author "Walsh, P. G." Journal mathematics of computation
9 results on '"Walsh, P. G."'

6. Corrigendum to ''On two classes of simultaneous Pell equations with no solutions''.

Author

Walsh, P. G.

Subjects
*SIMULTANEOUS equations, *DIOPHANTINE equations, *MATHEMATICS
Abstract

In this short note, we identify an error made in an earlier paper [Math. Comp. 68 (1999), no. 225, pp. 385–388] on simultaneous Pell equations, provide a revised statement of the main results contained therein, and show how this modification lends itself to the correctness of the proofs given in the earlier paper. [ABSTRACT FROM AUTHOR]

Published
2021
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8. A computational approach for solving $y^2=1^k+2^k+\dotsb+x^k$

Author

Jr., M. J. Jacobson, Pintér, Á., and Walsh, P. G.

Abstract

We present a computational approach for finding all integral solutions of the equation $y^2=1^k+2^k+\dotsb+x^k$ for even values of $k$. By reducing this problem to that of finding integral solutions of a certain class of quartic equations closely related to the Pell equations, we are able to apply the powerful computational machinery related to quadratic number fields. Using our approach, we determine all integral solutions for $2\le k\le 70$ assuming the Generalized Riemann Hypothesis, and for $2\le k\le 58$ unconditionally.

Published
2003

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