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= = (5) Let f be an irreducible polynomial of degree r in Fp[x] where p is an odd prime, and R = {[g]: geFp[x]}
= = (5) Let f be an irreducible polynomial of degree r in Fp[x] where p is an odd prime, and R = {[g]: geFp[x]} be the ring of congruence classes mod f. Let Qp = {G? ER*:G e R*} be the group of quadratic residues mod f. (a) Find #Qf in terms of p and r. (b) Let m:= - #Qf. Prove or disprove that Gm = 1 if and only if G EQf. = = (5) Let f be an irreducible polynomial of degree r in Fp[x] where p is an odd prime, and R = {[g]: geFp[x]} be the ring of congruence classes mod f. Let Qp = {G? ER*:G e R*} be the group of quadratic residues mod f. (a) Find #Qf in terms of p and r. (b) Let m:= - #Qf. Prove or disprove that Gm = 1 if and only if G EQf
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