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The
Legendre (a/p) symbol is usually not defined for p=2. Moreover, the extended definition given here is not consistent with the Kronecker symbol. E.g., the Kronecker symbol (a/2) is either 1,0,-1 depending on a. But the Kronecker symbols is an extension of the Legendre and Jacobi symbol. Anyone
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It does not behave in the expected way. Basically, the whole point of the
Legendre symbol is to have a convenient notation for quadratic reciprocity and similar properties of quadratic residues. That is, we are dealing with polynomial (quadratic) equations modulo a prime, and in such situations
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Speaking as a reader unfamiliar with the topic and most of the topics referenced, I found it strange that 2 was excluded without even the slightest hint why. I'm sure there's a good reason for it, and this discussion gives a hint, but can anyone add an explanation (for the casual
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I wonder if we should add something about how the
Legendre symbol is expressed in various markup systems (HTML, Unicode, LaTeX), esp. since the name Legendre symbol suggests that the topic is notational. I've seen these markup issues being added to various math-related articles.
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The case p=2 is now removed from the definition. None of the references I checked defines the
Legendre symbol for p=2. Besides the inconsistency with the Kronecker symbol, also Euler's equation would not be true for p=2.
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I think there is a mistake here. The formula supposedly from Gauss, expressed in terms of the variable zeta, doesn't produce a result of 0 when it should.
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various oddities arise when the modulus divides the discriminant of the equation; in this particular case, the discriminant of
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mathematically-inclined-but-unfamiliar-with-this-stuff reader) of exactly how it is problematic or ambiguous? --
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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How can
Kronecker symbol be a generalization of Legnedre symbol?
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If you believe you are correct, change the page, be bold.
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Kronecker symbol be a generalization of
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