Assignment #3 Due: Wednesday June 8 Determine the values of \(\left(\frac{a}{7}\right)\) for \(a = 1,2,3,4,5,6\) by using Euler's criterion. Do the work by hand and write out the calculations. Finish the the verification of the formula for \(\left(\frac{2}{p}\right)\) by showing that If \(p\equiv 1 (mod\, 4)\), then \(\left(\frac{2}{p}\right)=1\) and If \(p\equiv -3 (mod \, 4)\), then \(\left(\frac{2}{p}\right)=-1\) Determine whether the following quadratic congruences have a solution. Do not solve them. \(x^2 + 14x-35 \equiv 0\, (mod\,337)\) \(x^2-64x+943 \equiv 0\,(mod\,3011)\) Prove that if \(p\) is a prime such that \( p\equiv 1\,(mod\,4)\) and \(q=2p+1\) is prime, then 2 is a primitive root mod \(q\). Prove that if \(p\) is a prime such that \( p\equiv 1\,(mod\,10)\), then 5 is a quadratic residue mod \(p\). Sage Cell to determine whether 11 is a quadradic residue mod 101