No subject

[David W. Wilson]

> In fact, it looks as if S = {0} U {(4^j)(8k+1):  j >= 0} . Presumably this
would extend to the nonnegative integers.

 

It should read "negative integers".

 

OK, I found something really interesting.

 

Using the characterization S = {0} U {(4^j)(8k+1):  j >= 0}, the negative
values of S are the negations of A004215, the values that require 4 squares.
If this characterization is true, then n > 0 requires 4 squares precisely
when -n is a square mod 2^k for every k >= 0. I struggle to grok this.

 

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