query: Every prime divisor ($p \neq 5$) of $n^2+n-1$ is of the form $10k+9$
positive_passages.docid: 23606
positive_passages.text: Prime divisors of the integer $n^2+n-1$ (using the Legendre symbol)
negative_passages.docid: 154475
negative_passages.text: Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number
negative_passages.docid: 55060
negative_passages.text: Prove that $n^2+n+41$ is prime for $n<40$
negative_passages.docid: 96062
negative_passages.text: Show $\underbrace{{111\cdots}1}_{{\small{p-1} \ 1's}}$ is divisible by $p$
negative_passages.docid: 47162
negative_passages.text: Proving there are infinitely many primes of the form $a2^k+1.$
negative_passages.docid: 78342
negative_passages.text: When is $\phi(n)$ a prime number?
negative_passages.docid: 58905
negative_passages.text: Proving infintely many primes of the form 6k-1
negative_passages.docid: 9787
negative_passages.text: Primitive roots modulo primes congruent to n!
negative_passages.docid: 12365
negative_passages.text: Show that every prime $p>3$ is either of the form $6n+1$ or of the form $6n+5$
negative_passages.docid: 134739
negative_passages.text: product of divisors of n as a power of n.
negative_passages.docid: 92737
negative_passages.text: primes whose difference is a multiple of $n$
negative_passages.docid: 31555
negative_passages.text: Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)
negative_passages.docid: 116970
negative_passages.text: On the number divisors of a number
negative_passages.docid: 98871
negative_passages.text: How to prove that if a prime divides a Fermat Number then $p=k\cdot 2^{n+2}+1$?
negative_passages.docid: 26588
negative_passages.text: Prove by induction that $10^n -1$ is divisible by 11 for every even natural number
negative_passages.docid: 23684
negative_passages.text: Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime
negative_passages.docid: 17660
negative_passages.text: Show that the odd prime divisors of $n^2+n+1$ are of form $6k+1$ (exclude 3)