query: How to prove that, if two numbers are equal $\mod2$ and$\mod3$ ,they are equal$\mod 6 $?
positive_passages.docid: 62750
positive_passages.text: Constant case CRT: $\,x\equiv a\pmod{\! 2},\ x\equiv a\pmod{\! 5}\iff x\equiv a\pmod{\!10}$
negative_passages.docid: 17176
negative_passages.text: Proof that $x^n \mod b = (x \mod b)^n$
negative_passages.docid: 111505
negative_passages.text: Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
negative_passages.docid: 110256
negative_passages.text: Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
negative_passages.docid: 29231
negative_passages.text: Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
negative_passages.docid: 152039
negative_passages.text: Prove that $a^{2^n}=1 \mod 2^{n+2}$
negative_passages.docid: 88036
negative_passages.text: Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$
negative_passages.docid: 153313
negative_passages.text: Prove that for all integers $ a $ and $ b $, if $ a $ divides $ b $, then $ a^{2} $ divides $ b^{2} $.
negative_passages.docid: 92518
negative_passages.text: mod Distributive Law, factoring $\!\!\bmod\!\!:$ $\ ab\bmod ac = a(b\bmod c)$
negative_passages.docid: 20161
negative_passages.text: Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.
negative_passages.docid: 6918
negative_passages.text: Primes congruent to 1 mod 6
negative_passages.docid: 48484
negative_passages.text: Prove that $6|a+b+c$ if and only if $6|a^3+b^3+c^3$
negative_passages.docid: 35167
negative_passages.text: Prove congruence using fermat's thm
negative_passages.docid: 68635
negative_passages.text: When is $2$ a quadratic residue mod $p$?
negative_passages.docid: 91044
negative_passages.text: Why is a number that is divisible by $2$ and $3$, also divisible by $6$?
negative_passages.docid: 90438
negative_passages.text: To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$
negative_passages.docid: 131241
negative_passages.text: primes congruent to 5 mod 6 and 1 mod p