Hi all,

today I found something curious...

Let X(m) be the number of distinct quadratic residues mod m. (A023105 for m=2^n)

Let Y(m) be the number of n < m that can be expressed as a sum of 4 squares, but not by a sum of less than four squares. (A004015)

Then it appears that X(2^n) == Y(2^n) + 2 for all n.

A simple Java test program can be found here:

https://github.com/TilmanNeumann/jav...f4Squares.java