Let 
be an odd prime and 
a positive integer not
divisible by 
.
Then for each positive odd integer 
, let 
be
 |
with 
,
and let 
be the number of even 
s. Then
 |
where 
is the Legendre symbol.
Gauss's Criterion
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References
Shanks, D. "Gauss's Criterion." §1.17 in Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 38-40, 1993.Referenced on Wolfram|Alpha
Gauss's CriterionCite this as:
Weisstein, Eric W. "Gauss's Criterion." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GausssCriterion.html