query: Prove that $a + 2b \equiv 0 \bmod 3$ is an equivalence relation
positive_passages.docid: 11342
positive_passages.text: Show that conguence $\bmod m\,$ is an equivalence relation
negative_passages.docid: 92518
negative_passages.text: mod Distributive Law, factoring $\!\!\bmod\!\!:$ $\ ab\bmod ac = a(b\bmod c)$
negative_passages.docid: 16687
negative_passages.text: Number of Equivalence relations of $\{1,2,3\}$
negative_passages.docid: 141369
negative_passages.text: If $a+b\equiv0\pmod m$ and $c+d\equiv 0\pmod m$ then $ac\equiv bd\pmod m$. Demonstration.
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: 135986
negative_passages.text: Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
negative_passages.docid: 62455
negative_passages.text: Prove Equivalence Relation in G
negative_passages.docid: 12636
negative_passages.text: Product Rule for mod operator: $ ab\bmod p = ((a\bmod p)(b\bmod p))\bmod p$
negative_passages.docid: 29231
negative_passages.text: Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
negative_passages.docid: 52354
negative_passages.text: Given a idempotent endomorphism, show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$
negative_passages.docid: 61103
negative_passages.text: Prove that $\mathbb{|Q| = |Q\times Q|}$
negative_passages.docid: 21250
negative_passages.text: Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
negative_passages.docid: 56143
negative_passages.text: Proof of a basic $AC_\omega$ equivalence
negative_passages.docid: 128060
negative_passages.text: Proof that the relation $5 \mid (a + 4b)$ is symmetric and transitive
negative_passages.docid: 24585
negative_passages.text: Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$
negative_passages.docid: 125868
negative_passages.text: Prove $a \equiv b \pmod{c} \implies a^n \equiv b^n \pmod{c}$.
negative_passages.docid: 61860
negative_passages.text: Show that if $a$ has order $3\bmod p$ then $a+1$ has order $6\bmod p$.