query: prime numbers and greatest common divisor
positive_passages.docid: 158025
positive_passages.text: Intuition of why $\gcd(a,b) = \gcd(b, a \pmod b)$?
negative_passages.docid: 56229
negative_passages.text: On the difference between consecutive primes
negative_passages.docid: 96376
negative_passages.text: Why do we notate the greatest common divisor of $a$ and $b$ as $(a,b)$?
negative_passages.docid: 36862
negative_passages.text: A question about proving that there is no greatest common divisor
negative_passages.docid: 152506
negative_passages.text: The greatest common divisor is the smallest positive linear combination
negative_passages.docid: 117098
negative_passages.text: Properties of the greatest common divisor: $\gcd(a, b) = \gcd(a, b-a)$ and $\gcd(a, b) = \gcd(a, b \text{ mod } a)$
negative_passages.docid: 44857
negative_passages.text: Why the $(n+1)$th prime number cannot exceed the smallest prime divisor of $p_1\dotsc p_n + 1$
negative_passages.docid: 78342
negative_passages.text: When is $\phi(n)$ a prime number?
negative_passages.docid: 151036
negative_passages.text: arithmetic progression of primes
negative_passages.docid: 132830
negative_passages.text: What place do prime numbers have in cryptography?
negative_passages.docid: 95533
negative_passages.text: I need some help with a GCD and LCM's Problem
negative_passages.docid: 124037
negative_passages.text: Complex prime numbers
negative_passages.docid: 45793
negative_passages.text: How do you prove a number is prime?
negative_passages.docid: 130944
negative_passages.text: Greatest common divisor of polynomials over $\mathbb{Q}$
negative_passages.docid: 152591
negative_passages.text: For which prime numbers $p$ does the congruence $x^2 + x + 1 \equiv 0 \pmod{p}$ have solutions?
negative_passages.docid: 4402
negative_passages.text: Group of order $pqr$, $p < q < r$ primes
negative_passages.docid: 63865
negative_passages.text: Fermat primality test $\gcd$ condition and carmichael numbers