# 12 times Sigma of 12 equals 14 times Sigma of 14

## Theorem

$x = 12$ and $y = 14$ are solutions to the indeterminate equation:

$x \ \sigma \left({x}\right) = y \ \sigma \left({y}\right)$

where $\sigma$ denotes the $\sigma$ function.

## Proof

 $\displaystyle 12 \ \sigma \left({12}\right)$ $=$ $\displaystyle 12 \times 28$ $\sigma$ of $12$ $\displaystyle$ $=$ $\displaystyle 12 \times 2 \times 14$ $\displaystyle$ $=$ $\displaystyle 14 \times 24$ $\displaystyle$ $=$ $\displaystyle 14 \ \sigma \left({14}\right)$ $\sigma$ of $14$

$\blacksquare$