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ON THE EQUATIONx(x+d)…(x+(k-1)d)=by2

Published online by Cambridge University Press:  01 May 2000

B. BRINDZA ,
L. HAJDU  and
I. Z. RUZSA
B. BRINDZA
Affiliation:
Institute of Mathematics and Informatics, Lajos Kossuth University, H-4010 Debrecen, PO Box 12, Hungary
L. HAJDU
Affiliation:
Institute of Mathematics and Informatics, Lajos Kossuth University, H-4010 Debrecen, PO Box 12, Hungary
I. Z. RUZSA
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, PO Box 127, H-1364 Budapest, Hungary
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Abstract

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In this paper we give a new bound for the solutionsx of the title equation, provided that k \ge 8. This bound is polynomial in d. Moreover, under the same condition, a similar bound for the number of solutions in (x, k, y, l) is given.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 2 , May 2000 , pp. 255 - 261
Copyright
2000 Glasgow Mathematical Journal Trust