# 12 times Divisor Sum of 12 equals 14 times Divisor Sum of 14

## Theorem

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

$x \, \map {\sigma_1} x = y \, \map {\sigma_1} y$

where $\sigma_1$ denotes the divisor sum function.

## Proof

 $\ds 12 \, \map {\sigma_1} {12}$ $=$ $\ds 12 \times 28$ $\sigma_1$ of $12$ $\ds$ $=$ $\ds 12 \times 2 \times 14$ $\ds$ $=$ $\ds 14 \times 24$ $\ds$ $=$ $\ds 14 \, \map {\sigma_1} {14}$ $\sigma_1$ of $14$

$\blacksquare$