Ive been working all afternoon on these two problems, and i dont have a clue how to solve either of them.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Let p>2 be a prime number and let n=2^{p}+1. Prove that |2|_{n}=2p.

Let p > 3 be a prime number and suppose there is an integer a such that a^{2}+a+1 ≡ 0 (mod p).

Prove that p≡1 (mod 3). (Hint: a^{3}−1=(a^{2}+a+1)(a−1))

2. Relevant equations

phi(x)=phi(p1)*phi(p2)...phi(pn) where p are the unique prime factors of x

3. The attempt at a solution

i dont even know where to begin, everything ive done ends with dead ends

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# Homework Help: Intro to modern algebra proof questions

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