Question

$50^{\text {th }}$ root of a number $x$ is $12$ and $50^{\text {th }}$ root of another number $y$ is $18$ . Then the remainder obtained on dividing $(x+y)$ by $25$ is_____

Answer 1

$ x + y =12^{50}+18^{50}=(150-6)^{25}+(325-1)^{25}$
$ =25 K -\left(6^{25}+1\right)=25 K -\left((5+1)^{25}+1\right) $
$ =25 K _1-2 $
Remainder $=23$