My first Gem!

Algebra Level 4

Is it possible to express $1^2 + 2^2 + 3^2 + \cdots + 50^2$ as $p^q\times q^p$ , where $p$ and $q$ are positive integers.

If yes then find $p+q$ .

Else submit your answer as $9999$

This is an original problem and belongs to the set My creations

1 solution

Skanda Prasad
Sep 18, 2017

Calculating the sum of the series from the formula for the sum of squares, we get the value to be equal to $42925$ .

The only possible way to express $42925$ as $p^{q}$ $\times$ $q^p$ is ( $1^{42925}\times 42925^1$ ).

Hence, $p+q=42926$