query: Is there any relation between $a\equiv x\pmod{b}$ and $a\equiv x\pmod{c}$?
positive_passages.docid: 21250
positive_passages.text: Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
negative_passages.docid: 67717
negative_passages.text: $A \oplus B = A \oplus C$ imply $B = C$?
negative_passages.docid: 84733
negative_passages.text: Why $a\equiv b\pmod n$ implies $a$ and $b$ have equal remainder when divided by $n$?
negative_passages.docid: 21737
negative_passages.text: If $A|B$ and $B|A$ then prove $A=\pm B$
negative_passages.docid: 66563
negative_passages.text: Is $ (A∪B)×(C∩D)=(A∪C)×(B∪D)$ true for all sets A,B,C and D?
negative_passages.docid: 46147
negative_passages.text: Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
negative_passages.docid: 17601
negative_passages.text: How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
negative_passages.docid: 113411
negative_passages.text: If $E$ is generated by $E_1$ and $E_2$, then $[E:F]\leq [E_1:F][E_2:F]$?
negative_passages.docid: 131155
negative_passages.text: $x\sim y\iff x^2\equiv y^2\pmod{\!6}$ is an equivalence relation.
negative_passages.docid: 978
negative_passages.text: Solving $ax \equiv c \pmod b$ efficiently when $a,b$ are not coprime
negative_passages.docid: 110703
negative_passages.text: How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
negative_passages.docid: 59442
negative_passages.text: Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
negative_passages.docid: 53915
negative_passages.text: prove that $a \equiv b \mod m$ is an equivalence relation on the integers
negative_passages.docid: 51153
negative_passages.text: Number of solutions to $x^2\equiv a\pmod m$
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: 60305
negative_passages.text: Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$
negative_passages.docid: 66748
negative_passages.text: Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$