Eulers criterion says that if p is a prime then ap12 ap mod

Euler\'s criterion says that if p is a prime, then a^(p-1)/2 = (a/p) (mod p). Use successive squaring to compute 11^(1729-1)/2 (mod 1729) and use Quadratic Reciprocity to compute (11/1729).

Euler\'s criterion says that if p is a prime, then a^(p-1)/2 = (a/p) (mod p).

11^(1729-1)/2 (mod 1729)

a= 11

p=1729

11^(1729-1)/2 (mod 1729) = 11/1729

11/1729=

since 1729=2(mod11) :

(11/1729)=(11/2)=?1

by definition of the Jacobi\'s Symbol:

1729=7?13?19?(11/1729)=(11/7)(11/13)(11/19)=(?(7/11))(2/11)(?(8?/?11))=?1

as 11?

$Euler\'s criterion says that if p is a prime, then a^(p-1)/2 = (a/p) (mod p). Use successive squaring to compute 11^(1729-1)/2 (mod 1729) and use Quadratic Reci$

Eulers criterion says that if p is a prime then ap12 ap mod

Solution

Get Help Now

Submit a Take Down Notice