legendre symbol वाक्य
उदाहरण वाक्य
मोबाइल
- The triple of primes are linked modulo 2 ( the R�dei symbol is " 1 ) but are pairwise unlinked modulo 2 ( the Legendre symbols are all 1 ).
- This is now known as the Legendre symbol, and an equivalent definition is used today : for all integers " a " and all odd primes " p"
- If the required quadratic nonresidue z is to be found by checking if a randomly taken number y is a quadratic nonresidue, it requires ( on average ) 2 computations of the Legendre symbol.
- The triple of primes are " linked " modulo 2 ( the R�dei symbol is " 1 ) but are " pairwise unlinked " modulo 2 ( the Legendre symbols are all 1 ).
- Just as the quadratic reciprocity law for the Legendre symbol is also true for the Jacobi symbol, the requirement that the numbers be prime is not needed; it suffices that they be odd relatively prime nonunits.
- Determining whether " a " is a quadratic residue or nonresidue modulo " n " ( denoted or ) can be done efficiently for prime " n " by computing the Legendre symbol.
- This is because given g ^ a and g ^ b, one can efficiently compute the Legendre symbol of g ^ { ab }, giving a successful method to distinguish g ^ { ab } from a random group element.
- The case originally considered by C . F . Gauss was the quadratic Gauss sum, for " R " the field of residues modulo a prime number " p ", and & chi; the Legendre symbol.
- But since half the numbers between 1 and " n " are nonresidues, picking numbers " x " at random and calculating the Legendre symbol ( " x " | " n " ) until a nonresidue is found will quickly produce one.
- The constant implicit in the notation is genus of the curve in question, and so ( Legendre symbol or hyperelliptic case ) can be taken as the degree of " F " . ( More general results, for other values of " N ", can be obtained starting from there .)
- The average of two computations of the Legendre symbol are explained as follows : y is a quadratic residue with chance \ tfrac { \ tfrac { p + 1 } { 2 } } { p } = \ tfrac { 1 + \ tfrac { 1 } { p } } { 2 }, which is smaller than 1 but \ geq \ tfrac { 1 } { 2 }, so we will on average need to check if a y is a quadratic residue two times.
- अधिक वाक्य: 1 2
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