Gauss's Criterion

Let p be an odd prime and b a positive integer not divisible by p. Then for each positive odd integer 2k-1<p, let r_k be

 r_k=(2k-1)b (mod p)

with 0<r_k<p, and let t be the number of even r_ks. Then


where (b/p) is the Legendre symbol.

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Shanks, D. "Gauss's Criterion." §1.17 in Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 38-40, 1993.

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Gauss's Criterion

Cite this as:

Weisstein, Eric W. "Gauss's Criterion." From MathWorld--A Wolfram Web Resource.

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