query: Distributive law of greatest common divisors.
positive_passages.docid: 147527
positive_passages.text: Let $a$ and $b$ be non-zero integers, and $c$ be an integer. Let $d = \gcd(a, b)$. Prove that if $a|c$ and $b|c$ then $ab|cd$.
negative_passages.docid: 81895
negative_passages.text: A generalisation of the fundamental theorem of algebra
negative_passages.docid: 72295
negative_passages.text: A difficulty in understanding the proof of distributivity of tensor products over direct sums for modules.
negative_passages.docid: 142693
negative_passages.text: $\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
negative_passages.docid: 139833
negative_passages.text: Prove that $\gcd(M, N)\times \mbox{lcm}(M, N) = M \times N$.
negative_passages.docid: 109070
negative_passages.text: Question about the proof of the distributive property for sets
negative_passages.docid: 134739
negative_passages.text: product of divisors of n as a power of n.
negative_passages.docid: 6410
negative_passages.text: Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]
negative_passages.docid: 1712
negative_passages.text: $ d_1,d_2\mid n\iff {\rm lcm}(d_1,d_2)\mid n\ $ [LCM Universal Property]
negative_passages.docid: 74924
negative_passages.text: identity element of $(D_n ,\gcd)$
negative_passages.docid: 63758
negative_passages.text: $c\mid ab\Rightarrow c\mid \gcd(a,c)\gcd(b,c),\,$ for integers $a, b, c$
negative_passages.docid: 45213
negative_passages.text: Easiest and most complex proof of $\gcd (a,b) \times \operatorname{lcm} (a,b) =ab.$
negative_passages.docid: 152506
negative_passages.text: The greatest common divisor is the smallest positive linear combination
negative_passages.docid: 42141
negative_passages.text: Proving Distributivity of Matrix Multiplication
negative_passages.docid: 59856
negative_passages.text: Find $x,y$ given $\gcd(x,y)$ and ${\rm lcm}(x,y)$
negative_passages.docid: 112486
negative_passages.text: Bounds on a sum of gcd's
negative_passages.docid: 82071
negative_passages.text: divisor of a product of integers is a product of divisors