Difference of two squares?

Number Theory Level 2

$(323948023948250948230948)_{31}$

Can the number above be written as the difference of two squares , i.e. $m^2 - n^2$ for integral values $m$ and $n$ ?

Note: The subscript denotes base 31.

No Yes

1 solution

Geoff Pilling
May 16, 2016

The number is odd, since for odd bases, the number is odd if there is an odd number of odd digits, and in this case there are $9$ odd digits. And, all odd numbers can be expressed as the difference of two squares. So, $\boxed{yes}$ it can be expressed as the difference of two squares.

Difference of two squares?

1 solution

0 pending reports