Jacobi symbol
Generalization of the Legendre symbol in number theory / From Wikipedia, the free encyclopedia
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The Jacobi symbol is a generalization of the Legendre symbol. Introduced by Jacobi in 1837,[1] it is of theoretical interest in modular arithmetic and other branches of number theory, but its main use is in computational number theory, especially primality testing and integer factorization; these in turn are important in cryptography.
More information kn ...
k n | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
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1 | 1 | ||||||||||||||||
3 | 0 | 1 | −1 | ||||||||||||||
5 | 0 | 1 | −1 | −1 | 1 | ||||||||||||
7 | 0 | 1 | 1 | −1 | 1 | −1 | −1 | ||||||||||
9 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | ||||||||
11 | 0 | 1 | −1 | 1 | 1 | 1 | −1 | −1 | −1 | 1 | −1 | ||||||
13 | 0 | 1 | −1 | 1 | 1 | −1 | −1 | −1 | −1 | 1 | 1 | −1 | 1 | ||||
15 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | −1 | 1 | 0 | 0 | −1 | 0 | −1 | −1 | ||
17 | −0 | −1 | 1 | −1 | −1 | −1 | −1 | −1 | 1 | −1 | −1 | −1 | −1 | 1 | −1 | 1 | 1 |
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