query: Show that if a and b are relatively prime, then their sum and product are also relatively prime.
positive_passages.docid: 20878
positive_passages.text: If $(a,b)=1$ then prove $(a+b, ab)=1$.
negative_passages.docid: 112644
negative_passages.text: The product of two numbers that can be written as the sum of two squares
negative_passages.docid: 125188
negative_passages.text: how to prove $m^{\phi(n)}+n^{\phi(m)}\equiv 1 \pmod{mn}$ where m and n are relatively prime?
negative_passages.docid: 834
negative_passages.text: If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.
negative_passages.docid: 27170
negative_passages.text: $a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
negative_passages.docid: 53475
negative_passages.text: Let $H$ have order $m$ and $K$ have order $n$, where $m$ and $n$ are relatively prime. Then $H \cap K=\{e\}$
negative_passages.docid: 120282
negative_passages.text: Sum of two co-prime integers
negative_passages.docid: 14162
negative_passages.text: How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$
negative_passages.docid: 33741
negative_passages.text: If $A\simeq\prod A_i$ then $\sum e_i=1$
negative_passages.docid: 150958
negative_passages.text: Group theory question. If $m$ and $n$ are relatively prime, and $a$, $b$ belong to group and $a^m = b^m$ and $a^n = b^n$, how would one prove $a = b$?
negative_passages.docid: 46383
negative_passages.text: If $x$ divides $z$, $y$ divides $z$ and $x$ and $y$ are relatively prime, then $xy$ divides $z$.
negative_passages.docid: 20823
negative_passages.text: If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
negative_passages.docid: 27250
negative_passages.text: Greatest common divisor of two relatively primes
negative_passages.docid: 344
negative_passages.text: Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.
negative_passages.docid: 141369
negative_passages.text: If $a+b\equiv0\pmod m$ and $c+d\equiv 0\pmod m$ then $ac\equiv bd\pmod m$. Demonstration.
negative_passages.docid: 107173
negative_passages.text: If $a\lt{b}$ and $c\le{d}$, prove that $a+c\lt b+d$
negative_passages.docid: 60804
negative_passages.text: About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime