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 w
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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