MathDB
10th ibmo - chile 1995/q1.

Source: Spanish Communities

May 7, 2006
number theorynumber theory unsolved

Problem Statement

Find all the possible values of the sum of the digits of all the perfect squares.
[Commented by djimenez] Comment: I would rewrite it as follows: Let f:N→Nf: \mathbb{N}\rightarrow \mathbb{N} such that f(n)f(n) is the sum of all the digits of the number n2n^2. Find the image of ff (where, by image it is understood the set of all xx such that exists an nn with f(n)=xf(n)=x).