[ Residue arithmetic (other).]

Find the remainder of $\left(116+17^{17}\right)^{21} \cdot 7^{49}$ when divided by 8.

#
$\left(116+17^{17}\right)^{21} \cdot 7^{49} \equiv\left(4+1^{17}\right)^{21} \cdot 7 \cdot 49^{24} \equiv 5^{21} \cdot(-1) \cdot 1^{24}=-5 \cdot 25^{10} \equiv-5 \cdot 1^{10} \equiv 3(\bmod 8)$.

Answer

## 3.