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Abstrakty
We show that, with suitable modification, the upper bound estimates of Stolt for the fundamental integer solutions of the Diophantine equation Au²+Buv+Cv²=N, where A>0, N≠0 and B²-4AC is positive and nonsquare, in fact characterize the fundamental solutions. As a corollary, we get a corresponding result for the equation u²-dv²=N, where d is positive and nonsquare, in which case the upper bound estimates were obtained by Nagell and Chebyshev.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
291-299
Opis fizyczny
Daty
wydano
2015
Twórcy
autor
- Department of Mathematics, University of Queensland, Brisbane 4072, Australia
- Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia
autor
- Actuarial and Economic Services Division, National Council on Compensation Insurance, Boca Raton, FL 33487, U.S.A.
autor
- Department of Mathematics, Saint Louis University - Madrid campus, Avenida del Valle 34, 28003 Madrid, Spain
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-3-4