- #1
DianaSagita
- 11
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Homework Statement
First of all, hi everyone!
I'm quite new in number theory, and need help on this one badly...
Determine all prime numbers p so p2 divides 5p2+1.
Homework Equations
Euler's theorem: If a and m are coprimes then [tex]a^{\varphi(m)}\equiv 1 (mod\ m)[/tex]
where [tex]\varphi(m)[/tex] (Euler's function) denotes number of positive integers which are coprime with m and not greater than given int m.
Special: Fermat's little theorem... if p is prime, p and a coprimes, then [tex]a^{p-1}\equiv 1 (mod\ p)[/tex]
...and... [tex]\varphi(p^{2})=p^{2}-p[/tex]
The Attempt at a Solution
Know one solution p=3, but I got it by assumption. :((
Thanks in advance!