A Fact

For discussing Olympiad Level Number Theory problems
mutasimmim
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A Fact

Unread post by mutasimmim » Fri Oct 03, 2014 10:36 pm

Prove that $2$ is a primitive root of $ 5^n$ for all positive integers $n$.

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SANZEED
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Re: A Fact

Unread post by SANZEED » Fri Oct 03, 2014 10:57 pm

Hint 1:
$a\equiv b(mod p^{k})\Rightarrow a^{p^{s}}\equiv b^{p^{s}}(mod p^{k+s})$. This should be proved first.
Hint 2:
$\phi(p^{n})=p^{n-1}\cdot (p-1)$
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