query: How to prove $\gcd(k^{(2^i)}+1,k^{(2^j)}+1)=1$?
positive_passages.docid: 20574
positive_passages.text: Understanding the proof for $\gcd (F_n, F_{n+k}) = 1$ where $F_n$ is a Fermat number
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: 84501
negative_passages.text: Proof involving Cyclic group, generator and GCD
negative_passages.docid: 7091
negative_passages.text: If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
negative_passages.docid: 97196
negative_passages.text: $k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}\,$ if $\,\gcd(l,k)=1$
negative_passages.docid: 122096
negative_passages.text: Find $GCD(n^2+1,n+1)$
negative_passages.docid: 84417
negative_passages.text: Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
negative_passages.docid: 74924
negative_passages.text: identity element of $(D_n ,\gcd)$
negative_passages.docid: 21788
negative_passages.text: Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
negative_passages.docid: 135086
negative_passages.text: GCD of two numbers divided by their greatest common divisor is 1
negative_passages.docid: 22845
negative_passages.text: Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
negative_passages.docid: 121156
negative_passages.text: Prove that: $\gcd[a,b,c]=\frac{abc.\operatorname{lcm}(a,b,c)}{\operatorname{lcm}(a,b)\operatorname{lcm}(a,c)\operatorname{lcm}(b,c)}$
negative_passages.docid: 20477
negative_passages.text: Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$
negative_passages.docid: 147246
negative_passages.text: If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
negative_passages.docid: 53777
negative_passages.text: Why is $\gcd(x^4+1,x^2-1) = 1$ but I get $2$? [unit normalization of gcds]
negative_passages.docid: 32344
negative_passages.text: Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.
negative_passages.docid: 157784
negative_passages.text: Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.