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A. Grytczuk, F. Luca and M. Wójtowicz, “The Negative Pell Equation and Pythagorean Triples,” Proceedings of the Japan Academy, Vol. 76, No. 6, 2000, pp. 91-94. doi:10.3792/pjaa.76.91

has been cited by the following article:

• TITLE: Gauss’ Problem, Negative Pell’s Equation and Odd Graphs

  AUTHORS: Aleksander Grytczuk

  KEYWORDS: Fermat Numbers, Class-Number Gauss’ Problem, Odd Graphs

  JOURNAL NAME: Advances in Pure Mathematics, Vol.1 No.4, July 26, 2011

  ABSTRACT: In this paper we present some results connected with still open problem of Gauss, negative Pell’s equation and some type graphs.In particular we prove in the Theorem 1 that all real quadratic fields K=Q( ) , generated by Fermat’s numbers with d=Fm+1=22m+1+1,m≥2, have not unique factorization. Theorem 2 give a connection of the Gauss problem with primitive Pythagorean triples. Moreover, in final part of our paper we indicate on some connections of the Gauss problem with odd graphs investigated by Cremona and Odoni in the papper [5].