MathDB
H 46

Source:

May 25, 2007
calculusintegrationDiophantine equationDiophantine Equations

Problem Statement

Let a,b,c,d,e,fa, b, c, d, e, f be integers such that b2−4ac>0b^{2}-4ac>0 is not a perfect square and 4acf+bde−ae2−cd2−fb2≠04acf+bde-ae^{2}-cd^{2}-fb^{2}\neq 0. Let f(x,y)=ax2+bxy+cy2+dx+ey+ff(x, y)=ax^{2}+bxy+cy^{2}+dx+ey+f Suppose that f(x,y)=0f(x, y)=0 has an integral solution. Show that f(x,y)=0f(x, y)=0 has infinitely many integral solutions.
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