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MATH 115B SOLUTION SET II APRIL 24, 2007 (1) Find the value of the following Legendre symbols: (a) (71/73) (b) (?219/383) (c) (3658/12703) Hint: 3658 2 ? 31 ? 59. Solution: (a) (71/73) (73/71) (2/71)
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How to fill out value of legendre symbol
To fill out the value of the Legendre symbol, you can follow these steps:
01
Determine the given number and the prime number with respect to which the symbol is being evaluated.
02
Apply Euler's Criterion, which states that the Legendre symbol can be calculated by raising the given number to the power of (p-1)/2, where p is the prime number.
03
Take this result modulo p. If the result is congruent to 1, then the Legendre symbol is 1. If the result is congruent to -1, then the Legendre symbol is -1.
04
Repeat this process for different prime numbers if required.
Who needs the value of the Legendre symbol?
01
Mathematicians and number theorists use the Legendre symbol to study quadratic residues and to solve various mathematical problems.
02
Cryptographers use Legendre symbols in cryptographic algorithms, such as the Quadratic Residue Cryptosystem, for secure communication and encryption purposes.
03
Engineers and scientists use Legendre symbols in various calculations and modeling where quadratic residues and number theory concepts are applicable.
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What is value of legendre symbol?
The Legendre symbol is a mathematical notation representing whether a number is a quadratic residue modulo a prime number.
Who is required to file value of legendre symbol?
The value of the Legendre symbol is primarily used by mathematicians and researchers working on number theory and related fields.
How to fill out value of legendre symbol?
To calculate the value of the Legendre symbol, denote it as (a/p), where 'a' is the integer and 'p' is the prime. It is filled out by determining if 'a' is a quadratic residue modulo 'p'.
What is the purpose of value of legendre symbol?
The purpose of the Legendre symbol is to indicate whether a given integer is a quadratic residue modulo a prime, aiding in various mathematical proofs and theorems.
What information must be reported on value of legendre symbol?
When reporting the value of the Legendre symbol, one must include the integer 'a', the prime 'p', and the calculated value of (a/p), indicating whether it's 1, -1, or 0.
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