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Old 2020-09-20, 12:23   #1
Till
 
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"Tilman Neumann"
Jan 2016
Germany

22·3·5·7 Posts
Default Quadratic residue counts related to four squares representation counts

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

Last fiddled with by Till on 2020-09-20 at 12:33 Reason: A023105
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