query: Why isn't $\gcd(x^2+3x+2,x^2+x)=(x+1)$? [unit normalization of gcds]
positive_passages.docid: 4425
positive_passages.text: Why are integer GCDs positive? [unit normalization of GCDs]
negative_passages.docid: 8160
negative_passages.text: What is $\gcd(0,a)$, where $a$ is a positive integer?
negative_passages.docid: 120459
negative_passages.text: Problem with finding the GCD in the Field of Polynomials mod p
negative_passages.docid: 10348
negative_passages.text: Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
negative_passages.docid: 83871
negative_passages.text: GCDs in integral domains are unique up to unit factors (associates)
negative_passages.docid: 6012
negative_passages.text: Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
negative_passages.docid: 136064
negative_passages.text: How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
negative_passages.docid: 23590
negative_passages.text: Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$
negative_passages.docid: 2208
negative_passages.text: $\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
negative_passages.docid: 84417
negative_passages.text: Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
negative_passages.docid: 34738
negative_passages.text: Prove that $\gcd(n!+1,(n+1)!+1)=1$
negative_passages.docid: 59006
negative_passages.text: Proof of $\gcd(n!+1, (n+1)!+1)=1$?
negative_passages.docid: 147307
negative_passages.text: How to evaluate $\sum_{\gcd (p,q)=1} \frac{1}{p^2q^2}$?
negative_passages.docid: 11388
negative_passages.text: How you get from $\gcd(a,b)=1 \Longleftrightarrow ax+by=1 \Longrightarrow a \nmid b$?
negative_passages.docid: 65218
negative_passages.text: Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
negative_passages.docid: 156641
negative_passages.text: Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
negative_passages.docid: 80148
negative_passages.text: Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$