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 Skip Navigation LinksMath Help > Number Theory > Theorems > Euler's Quadratic Residue Theorem

Euler's Quadratic Residue Theorem

A number, D, that is coprime to prime, p, is either a quadratic residue or nonresidue of p, depending on whether D(p-1)/2 is congruent (mod p) to ±1.

Internet references

 Mathworld: Euler's Quadratic Residue Theorem

Related pages in this website

Legendre symbol —  ( a

p
)  , where a is any integer, and p is an odd prime
Jacobi symbol —  ( a

n
)  , where a is any integer, and n is a positive integer greater than 2, an extension of the Legendre symbol.
Kronecker symbol —  ( a

n
)  , where a and n are any integers, an extension of the Jacobi symbol.

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