Question

$3\times 7^{22}+2\times 10^{22}-44$ when divided by 18 leaves the remainder _____

Answer 1

Answer: 15

$3(1+6{)}^{22}+2\cdot (1+9{)}^{22}-44$
$=(3+2-44)=18.I$
$=-39+18.I$
$=(54-39)+18(I-3)$
$=15+18I_1$
$\Rightarrow$ Remainder $=15$