Đáp án: $(x,y)\in\{(-6, -83), (-8, 125)\}$
Giải thích các bước giải:
Ta có:
$x^2+xy+5=7(x-y)$
$\to x^2+xy+5=7x-7y$
$\to x^2-7x+5=-xy-7y$
$\to x^2-7x+5=-y(x+7)$
$\to x^2-7x+5\quad\vdots\quad x+7$
$\to (x^2+7x)-(14x+98)-93\quad\vdots\quad x+7$
$\to x(x+7)-14(x+7)-93\quad\vdots\quad x+7$
$\to 93\quad\vdots\quad x+7$
$\to x+7\in U(93)$
$\to x+7\in\{1, 3, 31, 93, -1, -3, -31, -93\}$
$\to x\in\{-6, -4, 24, 86, -8, -10, -38, -100\}$
$\to y\in\{-83, -\dfrac{49}{3}, -\dfrac{413}{31}, \dfrac{-6799}{93}, 125, \dfrac{175}{3}, \dfrac{1715}{31}, \dfrac{10705}{93}\}$
Mà $x, y\in Z$
$\to (x,y)\in\{(-6, -83), (-8, 125)\}$
