query: Show that if $ p =2^n +1$ is a Fermat prime, then 3 is a primitive root modulo $p$
positive_passages.docid: 128575
positive_passages.text: Elementary proof that $3$ is a primitive root of a Fermat prime?
negative_passages.docid: 25034
negative_passages.text: Fermat numbers are coprime
negative_passages.docid: 26478
negative_passages.text: Show that the congruence $x^{p-1} \equiv 1 \pmod {p^2}$ has precisely $p-1$ solutions modulo $p^2$
negative_passages.docid: 15348
negative_passages.text: prime divisor of $3n+2$ proof
negative_passages.docid: 103323
negative_passages.text: Finding a primitive root of a prime number
negative_passages.docid: 9787
negative_passages.text: Primitive roots modulo primes congruent to n!
negative_passages.docid: 71788
negative_passages.text: Prove existence of multiplicative inverse modulo p when p is prime
negative_passages.docid: 146512
negative_passages.text: Prove that for every prime number $p>3$, $4p^2+1$ can be written as the sum of three square numbers
negative_passages.docid: 120629
negative_passages.text: Prove if $n$ has a primitive root, then it has exactly $\phi(\phi(n))$ of them
negative_passages.docid: 14724
negative_passages.text: For primes $p≡3\pmod 4$, prove that $[(p−1)/2]!≡±1\pmod p$.
negative_passages.docid: 37093
negative_passages.text: If p is an odd prime, prove that $1^2 \times 3^2 \times 5^2 \cdots  \times (p-2)^2 \equiv (-1)^{(p+1)/2}\pmod{p}$
negative_passages.docid: 131488
negative_passages.text: Show that $p^3+4$ is prime
negative_passages.docid: 125210
negative_passages.text: proof: primitive pythagorean triple, a or b has to be divisible by 3
negative_passages.docid: 130342
negative_passages.text: Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
negative_passages.docid: 74214
negative_passages.text: Prove that there are $p+1$ points on the elliptic curve $y^2 = x^3 + 1$ over $\mathbb{F}_p$, where $p > 3$ is a prime such that $p \equiv 2 \pmod 3$.
negative_passages.docid: 59416
negative_passages.text: Quadratic residues and index w.r.t. primitive root of a odd prime p
negative_passages.docid: 35167
negative_passages.text: Prove congruence using fermat's thm