query: Proving multiplicative inverse of modulo $m$ exists when $\gcd(m,x)=1$
positive_passages.docid: 31917
positive_passages.text: If $q$ is coprime to $a$ then $a\mid nq-1,\,$ so $q$ is invertible mod $a$
negative_passages.docid: 69967
negative_passages.text: How to prove $\gcd(a^m-b^m,a^n-b^n) = a^{\gcd(m,n)} - b^{\gcd(m,n)} $?
negative_passages.docid: 99815
negative_passages.text: Dividing versus multiplying by inverse in modular arithmetic
negative_passages.docid: 59566
negative_passages.text: Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
negative_passages.docid: 77278
negative_passages.text: If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
negative_passages.docid: 132587
negative_passages.text: Prove that the product of coprimes must be congruent to $-1$ or $1 \pmod{m}$
negative_passages.docid: 147902
negative_passages.text: Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$
negative_passages.docid: 7090
negative_passages.text: Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$
negative_passages.docid: 156966
negative_passages.text: Prove that if $b = dk$ where $gcd(m, a) = d$, there are $d$ solutions to $ax \equiv b \mod m$
negative_passages.docid: 108450
negative_passages.text: Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
negative_passages.docid: 19164
negative_passages.text: On the GCD of a Pair of Fermat Numbers
negative_passages.docid: 6410
negative_passages.text: Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]
negative_passages.docid: 18767
negative_passages.text: How do you find the modular inverse of $5\pmod{\!11}$
negative_passages.docid: 34323
negative_passages.text: Prove that $a^{(p-1)/2} \equiv 1$ (mod p) and $a^{(p-1)/2} \equiv -1 \pmod p$
negative_passages.docid: 18108
negative_passages.text: Show if $(a,p)=1$ there is a unique inverse of $a$ modulo $p$
negative_passages.docid: 64742
negative_passages.text: Prove a residue matrix $A$ (with coefficients in $\mathbb Z_n)$ has an inverse if and only if $\gcd(\det A,n) = 1$
negative_passages.docid: 55673
negative_passages.text: Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?