A number a is called a cubic residue modulo p if it is congruent to a cube modulo p, that is, if there is a number b such that a = b^3 (mod p).

A number a is called a cubic residue modulo p if it is congruent to a cube modulo p, that is, if there is a number b such that a = b^3 (mod p).(a) Make a list of all the cubic residues modulo 5, modulo 7, modulo 11, and modulo 13.(b) If p = 2 (mod 3), make a conjecture as to which a’s are cubic residues. Prove that your conjecture is correct.