$$x^2+x+3=0$$ Solve it in $$ \Bbb Z_{22} $$ Does there exist another method of solving this equation,besides making a table to calculate all the possibilities. Note that $$ 3,0 ∈\Bbb Z_{22} $$
2026-05-15 03:48:48.1778816928
Alternative solution for the following equation
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Notice that you want to find an $x$ such that $x^2 + x + 3 = 22k$ for some integer $k$.
Now, the right hand side of the equation is even. However if $x$ is only allowed to be an integer, no matter how you choose it that the left hand side will be odd. So there are no solutions in $\Bbb Z_{22}$.