query: Greatest common divisor / euclidean algorithm linear combination proof
positive_passages.docid: 152506
positive_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: 70951
negative_passages.text: Prove divisibility law $\,b\mid a,c\,\Rightarrow\, b\mid ka + lc$ for all $k,l\in\Bbb Z$
negative_passages.docid: 138072
negative_passages.text: Linear time algorithm for 2-SUM
negative_passages.docid: 63547
negative_passages.text: Euclid's Lemma and $\gcd(a,b)=1\Rightarrow \gcd(a^n,b^k)= 1$
negative_passages.docid: 83173
negative_passages.text: Prove linear combinations of logarithms of primes over $\mathbb{Q}$ is independent
negative_passages.docid: 149993
negative_passages.text: Use the Euclidean algorithm to prove that gcd(na, nb) = n gcd(a, b).
negative_passages.docid: 62959
negative_passages.text: How to find GCD, LCM on a set of numbers
negative_passages.docid: 22845
negative_passages.text: Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
negative_passages.docid: 157508
negative_passages.text: prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
negative_passages.docid: 15452
negative_passages.text: Proving determinant product rule combinatorially
negative_passages.docid: 137608
negative_passages.text: Proof of Euclid's formula for primitive Pythagorean Triples
negative_passages.docid: 30045
negative_passages.text: Solving linear congruences by hand: modular fractions and inverses
negative_passages.docid: 32350
negative_passages.text: Compilation of proofs for the summation of natural squares and cubes
negative_passages.docid: 72551
negative_passages.text: Proof that $\rho = \pm1$ implies linear combination
negative_passages.docid: 107095
negative_passages.text: Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$
negative_passages.docid: 122096
negative_passages.text: Find $GCD(n^2+1,n+1)$