query: If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
positive_passages.docid: 19046
positive_passages.text: Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n
negative_passages.docid: 92645
negative_passages.text: Why isn't $\gcd(x^2+3x+2,x^2+x)=(x+1)$? [unit normalization of gcds]
negative_passages.docid: 38295
negative_passages.text: If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
negative_passages.docid: 147527
negative_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: 84417
negative_passages.text: Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
negative_passages.docid: 128199
negative_passages.text: Proving gcd(a, a+2) is 1 or 2 for every integer a?
negative_passages.docid: 34738
negative_passages.text: Prove that $\gcd(n!+1,(n+1)!+1)=1$
negative_passages.docid: 158308
negative_passages.text: Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
negative_passages.docid: 82938
negative_passages.text: $\gcd(a,b)=1, x^a = y^b\Rightarrow x = n^b$, $ y = n^a$ for an integer $n$.
negative_passages.docid: 151434
negative_passages.text: If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
negative_passages.docid: 83307
negative_passages.text: If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
negative_passages.docid: 87846
negative_passages.text: If $\gcd (x,4) = 2$ and $\gcd(y,4) = 2$ then $\gcd(x+y,4) = 4$
negative_passages.docid: 1991
negative_passages.text: If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$
negative_passages.docid: 145354
negative_passages.text: What is $\gcd(0,0)$?
negative_passages.docid: 5708
negative_passages.text: Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
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: 49109
negative_passages.text: Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$