*PM : properties of the Legendre symbol, id = 8418 new !-- WP guess : properties of the Legendre symbol-- Status:
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*PM : properties of the Legendre symbol, id = 8418 new !-- WP guess : properties of the Legendre symbol-- Status:
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*PM : values of the Legendre symbol, id = 8425 new !-- WP guess : values of the Legendre symbol-- Status:
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*PM : values of the Legendre symbol, id = 8425 new !-- WP guess : values of the Legendre symbol-- Status:
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Simply pick an a and by computing the Legendre symbol ( a ^ 2-n | p ) one can see whether a satisfies the condition.
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In number theory, he conjectured the quadratic reciprocity law, subsequently proved by Gauss; in connection to this, the Legendre symbol is named after him.
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:Also, if you interpret the typographic construction monolithically, the legendre symbol might count . talk ) 13 : 54, 28 April 2011 ( UTC)
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The motivation for this definition is the fact that all prime numbers " n " satisfy the above equation, as explained in the Legendre symbol article.
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The notational convenience of the Legendre symbol inspired introduction of several other " symbols " used in algebraic number theory, such as the Hilbert symbol and the Artin symbol.
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It follows from the multiplicativity of the Legendre symbol that 2, & minus; 2 or & minus; 1 is a square modulo " p ".
