## Finding numbers for which the sum of the squares of the digits is a square

### Problem 171

Published on Saturday, 8th December 2007, 05:00 am; Solved by 1699; Difficulty rating: 65%For a positive integer `n`, let f(`n`) be the sum of the squares of the digits (in base 10) of `n`, e.g.

f(3) = 3^{2} = 9,

f(25) = 2^{2} + 5^{2} = 4 + 25 = 29,

f(442) = 4^{2} + 4^{2} + 2^{2} = 16 + 16 + 4 = 36

Find the last nine digits of the sum of all `n`, 0 < `n` < 10^{20}, such that f(`n`) is a perfect square.