# Math Help - Quad Reciprocity

Establish the following assertion: (5/p)=1 if and only if p=1, 9, 11, or 19(mod 20)

2. Originally Posted by cathwelch
Establish the following assertion: (5/p)=1 if and only if p=1, 9, 11, or 19(mod 20)
$\left ( \frac{5}{p} \right ) = \left ( \frac{p}{5} \right ) (-1)^{(p-1)(5-1)/4} = \left ( \frac{p}{5} \right )$

Therefore $p \equiv 1, 4 \pmod{5}$

Therefore $p \equiv 1, 4, 6,9, 11,14,16,19 \pmod{20}$

However, p is odd, therefore

$p \equiv 1, 9, 11, 19 \pmod{20}$

3. thanks, but did you use some sort of property or theorem

4. Never mind, I see that you used the Quadratic Reciprocity Law