problem; primitive root

Asked Nov 14 '16 at 11:08

Active Nov 14 '16 at 11:08

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a) There are as many primitive roots of $2p^n$ as $p^n$.

b) Any primitive root r of $p^n$ is also a primitive root of p.

c) A primitive root of $p^2$ is also a primitive root of $p^n$ for n >= 2.

Im so sorry . My professor teachs so quickly then I cant organize my thoughts... so It is better to see your solution and organize my ones.

finally do you know that there is a Burton's Elementary Number Theory solution?? I cant find that in google...

thnks!

asked Nov 14 '16 at 11:08

文奭允

For (a) see also http://math.stackexchange.com/questions/1994510/let-p-be-an-odd-prime-suppose-that-a-is-an-odd-integer-and-also-a-is-a-pr. – lhf Nov 14 '16 at 11:23
For (b) see http://math.stackexchange.com/questions/170648/prove-that-any-primitive-root-r-of-pn-is-also-a-primitive-root-of-p – Tengu Nov 14 '16 at 11:40
What exactly is the question here??? – barak manos Nov 14 '16 at 11:42
please solve... and doyou know there are solutions? :( – 文奭允 Nov 14 '16 at 11:46
Please solve what????? – barak manos Nov 14 '16 at 11:48
a...b...c... I think it is rude... sorry but maybe i need only c – 文奭允 Nov 14 '16 at 11:49
3

For c), there's http://math.stackexchange.com/questions/31679/if-g-is-a-primitive-root-of-p2-where-p-is-an-odd-prime-why-is-g-a-prim – Gerry Myerson Nov 14 '16 at 12:08
gosh how can do that...tell me – 文奭允 Nov 14 '16 at 12:20
a is not same thing :( – 文奭允 Nov 15 '16 at 02:18
I don't know what "how can do that" means, or what it refers to, or to whom it is addressed. – Gerry Myerson Nov 16 '16 at 04:53

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