Mathematics - Binomial Theorem Question with Solution | TestHub

$\begin{array}{rl}& 7^{103}=7\left(7^{102}\right)=7(343{)}^{34}=7(345-2{)}^{34}\\ & 7^{103}=23{\mathrm{K}}_1+7.2^{34}\end{array}$

Now $7.2^{34}=7.2^2\cdot 2^{32}$
$\begin{array}{rl}& =28\cdot (256{)}^4\\ & =28(253+3{)}^4\\ & \therefore 28\times 81\Rightarrow (23+5)(69+12)\\ & 23{\mathrm{K}}_2+60\\ & \therefore \text{ Remainder }=14\end{array}$