On the Solvability of a Family of Diophantine Equations
نویسندگان
چکیده
A frequently occurring problem in the theory of binary quadratic forms is to determine, for a given integer m, the existence of solutions to the Diophantine equation f(x, y): = ax + hxy + cy = m, having discriminant A = b 4ac. In the case of a strictly positive nonsquare discriminant, it is well known that the occurrence of one solution to f(x,y) = m implies the existence of infinitely many other solutions. Using this fact, one may attempt to investigate the solvability of the following family of binomial Diophantine equations,
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تاریخ انتشار 1999