Find all odd primes p for which \left(\frac{11}{p}\right) = 1. \left(\frac{11}{p}\right) is in Legendre Symbol.

\left(\frac{11}{p}\right) = - \left( \frac{p}{11} \right) due to quadratic reciprocity. ( 11 \equiv 3 \pmod{4})

Since 11 is prime and p is prime, we have gcd(11, p) = 1.

Apply Gauss' theorem.

\frac{11 - 1}{2} = 5.
Let S = \{p, 2p, 3p, 4p, 5p \}.
Let k = \{ s | s > 5 \}
Then \left(\frac{p}{11}\right) = (-1)^k = -1 iff k is odd.

When p = 3, k = 4.
When p = 5, k = 4.
For all odd primes p > 5, k = 5.

So all odd primes p > 5 satisfy \left(\frac{11}{p}\right) = 1.

Is my attempt correct?