# square modulo the prime...

• Apr 12th 2010, 05:10 AM
NikoBellic
square modulo the prime...
Determine whether 219 is a square modulo the prime 383.
• Apr 12th 2010, 08:10 AM
tonio
Quote:

Originally Posted by NikoBellic
Determine whether 219 is a square modulo the prime 383.

Using Jacobi's symbol and quadratic reciprocity:

$\binom {219}{383}=\binom{3}{383}\binom{73}{383}=-\binom{383}{3}\binom{383}{73}$ $=-\binom{2}{3}\binom{18}{73}=-(-1)\binom{2}{73}\binom{9}{73}=1\cdot 1\cdot 1=1$
Tonio