Use the law of quadratic reciprocity to show that if p is

Question

Please, do it step by step And can you do it quickly, the assignment

Find the least complete solution

1. x³ + x² + 1 ≡ 0 (mod 27)

Find the least complete solution to the congruence.

Start by making a table of the least residues of 1², 2², ....... 8² (mod 17)

2. 5x² + 11x -2 ≡ 0 (mod 27)

3. Use the law of quadratic reciprocity to show that if p is an odd prime other than 5, then (5/p) = 1 if and only if the last digit of p is 1 or 9.