query: Find three natural numbers $a,b,c$ such : $\begin{cases}ab=1(\mod c)\\ac=1(\mod b)\\bc=1(\mod a)\end{cases}$
positive_passages.docid: 4943
positive_passages.text: If $p,q,r$ are all primes,and $p|qr-1$,$q|pr-1$ and $r|pq-1$,find all possible values of $pqr$.
negative_passages.docid: 95409
negative_passages.text: Find no. of non negative integer solutions of $a+2b+3c = 200$
negative_passages.docid: 115719
negative_passages.text: Find the possible values of |A + B + C |
negative_passages.docid: 17677
negative_passages.text: Prove or show a counter example for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$
negative_passages.docid: 61210
negative_passages.text: BMO2 1995 Question 1 - Solve the equation for positive integers (a,b,c)
negative_passages.docid: 29078
negative_passages.text: find all the values of a and b so that the system has a) no solution b) 1 solution c) exactly 3 solutions and 4) infinitely many solutions
negative_passages.docid: 134493
negative_passages.text: Find the value of $ab+ 2cb+\sqrt3 ac$?
negative_passages.docid: 156468
negative_passages.text: Solutions to $a+b+c=12$, $a, b, c \in \mathbb{N}_0$
negative_passages.docid: 109745
negative_passages.text: If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
negative_passages.docid: 147246
negative_passages.text: If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
negative_passages.docid: 47737
negative_passages.text: Find all the possible values of $(a,b,c,d)$.
negative_passages.docid: 92518
negative_passages.text: mod Distributive Law, factoring $\!\!\bmod\!\!:$ $\ ab\bmod ac = a(b\bmod c)$
negative_passages.docid: 124995
negative_passages.text: $p\equiv 1,2,3\text{ mod }8 \Rightarrow p=a^2+2b^2\text{ for some $a,b\in\mathbb{Z}$.}$
negative_passages.docid: 115504
negative_passages.text: Find the value of a+b+c
negative_passages.docid: 124320
negative_passages.text: $a,b,c>0 \text{ s.t. }a+b+c=1 \implies \sqrt{ab+c}+\sqrt{bc+a}+\sqrt{ca+b} \ge 1+ \sqrt{ab}+\sqrt{bc}+\sqrt{ca}$
negative_passages.docid: 39563
negative_passages.text: How to show $a,b$ coprime to $n\Rightarrow ab$ coprime to $n$?
negative_passages.docid: 41792
negative_passages.text: If $abc=1$, then $\frac{a^{n+2}}{a^n+(n-1)b^n}+\frac{b^{n+2}}{b^n+(n-1)c^n}+\frac{c^{n+2}}{c^n+(n-1)a^n} \geq \frac{3}{n} $