$(8\%)$ If $m$ is a positive integer, the integer $a$ is a quadratic residue of $m$ if $gcd(a,m)=1$

and the congruence $x^2-=a(modm)$ has a solution. In other words, a quadratic residue

of $m$ is an integer relatively prime to $m$ that is a perfect square modulo $m.$ For example,

$2$ is a quadratic residue of $7$ because $gcd(2,7)=1$ and $3^2-=2(mod7).$ In addition, $3$ is

a quadratic nonresidue of $7$ because $gcd(3,7)=1$ and $x^2-=3(mod7)$ has no solution.

$($a$)(4\%)$ Which integers are quadratic residues of $11?$

$($b$)(4\%)$ Show that if $p$ is an odd prime and $a$ is an integer not divisible by $p,$ then

the congruence $x^2-=a(modp)$ has either no solutions or exactly two incogruent

solutions modulo $p.$