query: Unable to understand why gcd(bt+r,b)=gcd(b,r)
positive_passages.docid: 66748
positive_passages.text: Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
negative_passages.docid: 63965
negative_passages.text: How can I compute the sum of $ {m\over\gcd(m,n)}$?
negative_passages.docid: 85688
negative_passages.text: How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
negative_passages.docid: 24845
negative_passages.text: Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
negative_passages.docid: 77278
negative_passages.text: If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
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: 18714
negative_passages.text: $\gcd\left(a+b,\frac{a^p+b^p}{a+b}\right)=1$, or $p$
negative_passages.docid: 147802
negative_passages.text: Proving that $\gcd\left(\frac a {\gcd(a,b)},\frac b {\gcd(a,b)}\right) =1$
negative_passages.docid: 18772
negative_passages.text: If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
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: 14693
negative_passages.text: $d = \gcd(c,m),\ ac≡bc\pmod{\! m}\Rightarrow a≡b\pmod {\!m/d}\ $ [Congruence Cancellation & Division Rule]
negative_passages.docid: 52461
negative_passages.text: Why does $(g^b \bmod m)^a \bmod m = (g^a \bmod m)^b \bmod m$?
negative_passages.docid: 5789
negative_passages.text: $ d = \gcd(a,b)\Rightarrow\ \gcd(a/d,b/d) = 1$
negative_passages.docid: 96376
negative_passages.text: Why do we notate the greatest common divisor of $a$ and $b$ as $(a,b)$?
negative_passages.docid: 38547
negative_passages.text: Why does the Euclidean algorithm for finding GCD work?
negative_passages.docid: 35945
negative_passages.text: Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
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 $\gcd(a/d,b/d)=1$