Find all integers $k>2$ such that $5\equiv k \bmod k^2$.
I ended up with quardratic formula. Is it right?
Find all integers $k>2$ such that $5\equiv k \bmod k^2$.
I ended up with quardratic formula. Is it right?
$k^2|k-5$
so $k|k-5$
so
$k|5$
And since we stipulate $k>2$, we only need check $k=5$.
If $k>5$, then $k^2 > k - 5 > 0$, so $k-5$ can't be divisible by $k^2$; so the proposition is false. Since you were asked for integers $>2$, the only possibilities are 3, 4 and 5. A quick check reveals that 3 and 4 don't work, but 5 does; so the only possible value is $k=5$.