data/problems/171.yml
---
:id: 171
:name: Finding numbers for which the sum of the squares of the digits is a square
:url: https://projecteuler.net/problem=171
:content: "For a positive integer <var>n</var>, let f(<var>n</var>) be the sum of
the squares of the digits (in base 10) of <var>n</var>, e.g.\n\nf(3) = 3<sup>2</sup>
= 9, \nf(25) = 2<sup>2</sup> + 5<sup>2</sup> = 4 + 25 = 29, \nf(442) = 4<sup>2</sup>
+ 4<sup>2</sup> + 2<sup>2</sup> = 16 + 16 + 4 = 36\n\nFind the last nine digits
of the sum of all <var>n</var>, 0 \\< <var>n</var> \\< 10<sup>20</sup>, such that
f(<var>n</var>) is a perfect square.\n\n"