1.I.1H

Number Theory
Part II, 2006

State the theorem of the primitive root for an odd prime power modulus.

Prove that 3 is a primitive root modulo 7n7^{n} for all integers n1n \geqslant 1. Is 2 a primitive root modulo 7n7^{n} for all integers n1n \geqslant 1 ?

Prove that there is no primitive root modulo 8 .