Euler's Criterion

For p an odd prime and a positive integer a which is not a multiple of p,

 a^((p-1)/2)=(a/p) (mod p),

where (a|p) is the Legendre symbol.

See also

Legendre Symbol, Quadratic Residue

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Nagell, T. "Euler's Criterion and Legendre's Symbol." §38 in Introduction to Number Theory. New York: Wiley, pp. 133-136, 1951.Rosen, K. H. Ch. 9 in Elementary Number Theory and Its Applications, 3rd ed. Reading, MA: Addison-Wesley, 1993.Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 33-37, 1993.Wagon, S. Mathematica in Action. New York: W. H. Freeman, p. 293, 1991.

Referenced on Wolfram|Alpha

Euler's Criterion

Cite this as:

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

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