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The Legendre symbol is used ... by mathematicians in attempts to woo women. (If this is not right, please correct it.) |
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The Legendre symbol is used by mathematicians in the theory of numbers, particularly in the fields of factorization? and [quadratic residues]?. |
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Furthermore, if a is devisible by p we say (a/p) = 0. |
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Furthermore, if a is divisible by p we say (a/p) = 0. |
If p is a prime number and a is an integer relatively prime to p, then we define the Legendre? symbol (a/p) to be:
1 if a is a square modulo p (that is to say there exists an integer x such that x2 = a mod p)
-1 if a is not a square modulo p.
Furthermore, if a is divisible by p we say (a/p) = 0.
Euler proved that (a/p) = a((p-1)/2) mod p. Thus we can see that the Legendre symbol is multiplicative, i.e. (ab/p) = (a/p)(b/p).
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