Transcription of GAZETA MATEMATICA˘ - SSMR
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GAZETA MATEMATICA˘ - SSMR
GAZETA MATEMATIC ASERIA AANUL XXXIV (CXIII)Nr. 1 2/ 2016 ARTICOLEOn a two parameter class of quadratic Diophantine equations Arp ad B enyi1),2),Ioan Cas u3)Abstract. We characterize the solution set of a two parameter class ofquadratic Diophantine equations. Our proof relies on the solvability of thepositive Pell :Diophantine equation, quadratic equation, Pell equationMSC:Primary 11D09; Secondary this note we will be interested in exploring the solutionsof quadraticDiophantine equations of the formax2+by2+cx+dy+f= 0,wherea, b, c, d, f Z. Naturally, there is no hope in solving such a problemfor arbitrary coefficients, and simple examples show that there are such equa-tions which have zero, finitely many or infinitely many solutions (x, y) Z , we can see this to be the case by inspecting thelattice pointssitting on the algebraic curve defined by the quadratic equation above, butthis geometric intuition is not the one we will be using motiva-tion for this note stems from the following two problems proposed at the 7 8grade level:[3].
2 Articole We wish to show that the intuition behind these problems lends itself nicely to completely solving a two parameter class of quadratic Diophantine
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