\[
\left.\begin{array}{c}
\text { Division with remainder } \\
{[\text { Arithmetic of remainders (other).] }}
\end{array}\right]
\]

a) For which integers $n$ is the number $5 n^{2}+10 n+8$ divisible by 3?

b) And for which integers is it divisible by 4?
a) $5 n^{2}+10 n+8 \equiv-n^{2}-2 n-1=-(n+1)^{2}(\bmod 3)$.

b) $5 n^{2}+10 n+8 \equiv n^{2}+2 n=n(n+2)(\bmod 4)$.

## Answer

Divisible by 3 when $n=2+3 k$; by 4 when $n=2 k(k \in \mathbf{Z}$).