p.lazarov06 wrote: Given is the equation: \[x^2+mx+2022=0\]a) Find all the values of the parameter $m$, such that the two solutions of the equation $x_1, x_2$ are \textbf{natural} numbers WLOG $x_1\le x_2$ $x_1x_2=2022$ and so $(x_1,x_2)\in\{(1,2022),(2,1011),(3,674),(6,337)\}$ And so $\boxed{m=-x_1-x_2\in\{-2023,-1013,-677,-343\}}$ p.lazarov06 wrote: b)Find all the values of the parameter $m$, such that the two solutions of the equation $x_1, x_2$ are \textbf{integer} numbers WLOG $|x_1|\le |x_2|$ $x_1x_2=2022$ and so $(x_1,x_2)\in\{(1,2022),(2,1011),(3,674),(6,337),(-1,-2022),(-2,-1011),(-3,-674),(-6,-337)\}$ And so $\boxed{m=-x_1-x_2\in\{-2023,-1013,-677,-343,343,677,1013,2023\}}$