I am trying to find relation of pairs $(x,y)$ and $(x_1,y_1)$ such that $f(x,y)\equiv f(x_1,y_1)(\mbox{mod }n)$ where $f$ is a quadratic expression like $ax^2+bxy+cy^2+dx+ey+f$ Thanks in advance
Quadratic equation congruence
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number-theory