query: Formula for one element in the intersection of two cosets $m\Bbb{Z} + a$ and $n \Bbb{Z} + b$ whenever $\gcd(m,n) = 1$ is true.
positive_passages.docid: 145835
positive_passages.text: Closed form for CRT solution using Euler $\phi\,$ (totient)
negative_passages.docid: 72747
negative_passages.text: Proving gcd($a,b$)lcm($a,b$) = $|ab|$
negative_passages.docid: 37596
negative_passages.text: If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
negative_passages.docid: 49578
negative_passages.text: Proving $a\mathbb{Z}\cap b\mathbb{Z}=[a,b]\mathbb{Z}$
negative_passages.docid: 112084
negative_passages.text: Proof of a formula for the power set of a union of two sets
negative_passages.docid: 52483
negative_passages.text: Showing that $(m)\cap (n)=(\operatorname{lcm}(m,n))$ and $(m)+(n)=(\gcd(m,n))$ for any $m,n\in\mathbb{Z}$
negative_passages.docid: 32108
negative_passages.text: $ a\in \Bbb Z_n$ is invertible $\,\Rightarrow\gcd (a,n) =1$
negative_passages.docid: 66748
negative_passages.text: Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
negative_passages.docid: 74924
negative_passages.text: identity element of $(D_n ,\gcd)$
negative_passages.docid: 11600
negative_passages.text: $\gcd(a,\operatorname{lcm}(b,c))=\operatorname{lcm}(\gcd(a,b),\gcd(a,c))$
negative_passages.docid: 63965
negative_passages.text: How can I compute the sum of $ {m\over\gcd(m,n)}$?
negative_passages.docid: 50396
negative_passages.text: How can I show that $ab \sim \gcd (a,b) {\operatorname{lcm} (a,b)}$ for any $a,b \in R \setminus \{0\}$?
negative_passages.docid: 20823
negative_passages.text: If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
negative_passages.docid: 78678
negative_passages.text: If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
negative_passages.docid: 2208
negative_passages.text: $\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
negative_passages.docid: 67660
negative_passages.text: Prove $\,b\equiv c\pmod{\!m}\Rightarrow \gcd(b,m)=\gcd(c,m)$ i.e. $\gcd(c+km,m) = \gcd(c,m)$
negative_passages.docid: 74077
negative_passages.text: A intersection (A union B)