Question: $3 \times 7^{22}+2 \times 10^{22}-44$ when divided by 18 leaves the remainder
Solution:
$3(1+6)^{22}+2 \cdot(1+9)^{22}-44=(3+2-44)=18 . \mathrm{I}$
$=-39+18 . \mathrm{I}$
$=(54-39)+18(\mathrm{I}-3)$
$=15+18 \mathrm{I}_{1}$
$\Rightarrow$ Remainder $=15$
