# Symmetric number

Take a integer $n$ between 10 and 99. We write $n=10x+y$ with $x, y$ between 0 and 9.  We define the symmetric number $\bar n=10y+x$. For example, if $n=74$ then $\bar n=47$.

It is then easy to show that the difference of the square $n^2 -\bar n ^2$ can be express as the sum of differences between $3$ digits symmetric numbers.

$n^2 -\bar n ^2=10(m-\bar m)+(m'-\bar m')$ with

$m=100a_x+a_y$ and $m'=100b_x+b_y$, with $x^2=10a_x+b_x$ and $y^2=10a_y+b_y$.

For example with $n=74$ we have $7^2=4\times 10+9$ and $4^2=16$, leads to

$74^2-47^2=10\times(401-104)+(906-609)$