query: Prove that $7$ is a primitive root modulo $p=2^s+1$.
positive_passages.docid: 17919
positive_passages.text: For every prime of the form $2^{4n}+1$, 7 is a primitive root.
negative_passages.docid: 64453
negative_passages.text: Prove if $(a,p)=1$, then $\{a,2a,3a,...,pa\}$ is a complete residue system modulo $p$.
negative_passages.docid: 77806
negative_passages.text: Proving if $a$ is not a multiple of prime $p$, then an integer $b$ exists such that $p^b - 1$ is a multiple of $a$
negative_passages.docid: 127205
negative_passages.text: Explain proof of irreducibility of $x^{p-1} + 2x^{p-2}+ \dots +(p-1)x + p$
negative_passages.docid: 127833
negative_passages.text: Proving that $7^n(3n+1)-1$ is divisible by 9
negative_passages.docid: 41641
negative_passages.text: $(n-7)(n+7)=$ some perfect square
negative_passages.docid: 6160
negative_passages.text: How to prove a number $a$ is quadratic residue modulo $n$?
negative_passages.docid: 41312
negative_passages.text: Question on primitive roots of unity
negative_passages.docid: 111505
negative_passages.text: Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
negative_passages.docid: 69682
negative_passages.text: Roots of $y=x^3+x^2-6x-7$
negative_passages.docid: 51520
negative_passages.text: Prove that the only prime triple is 3, 5, 7
negative_passages.docid: 109860
negative_passages.text: Is the number $7$ a polynomial expression.
negative_passages.docid: 68275
negative_passages.text: Primitive Root Theorem Proof
negative_passages.docid: 110752
negative_passages.text: $g^\frac{p-1}{2} \equiv -1 \ (mod \ p)$
negative_passages.docid: 93898
negative_passages.text: Prove that for any prime p, there is a complete set of mod p residues {q1, . . . , qp}, where each qi is prime.
negative_passages.docid: 24053
negative_passages.text: How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
negative_passages.docid: 17194
negative_passages.text: $6^{(n+2)} + 7^{(2n+1)}$ is divisible by $43$ for $n \ge 1$