关于一类二次不定方程
On a Class of Quadratic Diophantine Equations
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摘要: 证明了不定方程x^2-kxy+y^2+lx=0,l\in \3,5\, k\in N^+时, 有无穷多个正整数解(x,y)当且仅当k与l的取值为(k,l)=(3,3),(4,3),(5,3),(3,5),(5,5),(7,5).Abstract: It is proved that the Diophantine equations x^2-kxy+y^2+lx=0, l\in \3,5\ have infinite number of positive integer solutions (x, y) if and only if (k,l)=(3,3),(4,3),(5,3),(3,5),(5,5),(7,5).
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