query: Divisibility proof with coprimes of 6
positive_passages.docid: 26503
positive_passages.text: Suppose that $p$ ≥ $q$ ≥ $5$ are both prime numbers. Prove that 24 divides ($p^2 − q^2$)
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: 77064
negative_passages.text: Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
negative_passages.docid: 41295
negative_passages.text: Divisibility, LCM and GCD for fractions (rationals)
negative_passages.docid: 50670
negative_passages.text: Use Mathematical Induction to prove 6 divides $n(n+1)(2n+1)$
negative_passages.docid: 94958
negative_passages.text: Prob. 6 (d), Chap. 1, in Baby Rudin, 3rd ed: How to complete this proof?
negative_passages.docid: 107725
negative_passages.text: Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$
negative_passages.docid: 77430
negative_passages.text: Prove that every prime larger than $3$ gives a remainder of $1$ or $5$ if divided by $6$
negative_passages.docid: 119152
negative_passages.text: Proving irreducibility of $x^6-72$
negative_passages.docid: 124240
negative_passages.text: Inductive proof of $\,9 \mathrel| 4^n+6n-1\,$ for all $\,n\in\Bbb N$
negative_passages.docid: 11500
negative_passages.text: Divisibility by 7 rule, and Congruence Arithmetic Laws
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: 61860
negative_passages.text: Show that if $a$ has order $3\bmod p$ then $a+1$ has order $6\bmod p$.
negative_passages.docid: 59135
negative_passages.text: What is the proof of divisibility by $13$?
negative_passages.docid: 33052
negative_passages.text: How to prove $\bar{m}$ is a zero divisor in $\mathbb{Z}_n$ if and only if $m,n$ are not coprime
negative_passages.docid: 12365
negative_passages.text: Show that every prime $p>3$ is either of the form $6n+1$ or of the form $6n+5$
negative_passages.docid: 49501
negative_passages.text: Prove that : $(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)$ divisible by $12$