Gauss’ Problem, Negative Pell’s Equation and Odd Graphs

DOI: 10.4236/apm.2011.14026   PDF   HTML     3,945 Downloads   8,900 Views  


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].

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A. Grytczuk, "Gauss’ Problem, Negative Pell’s Equation and Odd Graphs," Advances in Pure Mathematics, Vol. 1 No. 4, 2011, pp. 133-135. doi: 10.4236/apm.2011.14026.

Conflicts of Interest

The authors declare no conflicts of interest.


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