query: If I know that $b$ is a multiple of $32$ then how can i show that $b+5$ and $b^2 + 7$ are coprime?
positive_passages.docid: 23684
positive_passages.text: Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime
negative_passages.docid: 11168
negative_passages.text: Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
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: 139350
negative_passages.text: Given two coprime integers, find multiples of them that differ by 1
negative_passages.docid: 156577
negative_passages.text: The cube of any number not a multiple of $7$, will equal one more or one less than a multiple of $7$
negative_passages.docid: 51520
negative_passages.text: Prove that the only prime triple is 3, 5, 7
negative_passages.docid: 33998
negative_passages.text: Show that given seven real numbers, it is always possible take two of them, such that $\left\vert\frac{a-b}{1+ab}\right\vert<\frac{1}{\sqrt{3}}$
negative_passages.docid: 127237
negative_passages.text: Let $I = \{a +ib \in \Bbb Z[i] : a$ and $b$ are both multiple of $5\}$.
negative_passages.docid: 77806
negative_passages.text: Proving if $a$ is not a multiple of prime $p$, then an integer $b$ exists such that $p^b - 1$ is a multiple of $a$
negative_passages.docid: 121918
negative_passages.text: Why is $5^{n+1}+2\cdot 3^n+1$ a multiple of $8$ for every natural number $n$?
negative_passages.docid: 11500
negative_passages.text: Divisibility by 7 rule, and Congruence Arithmetic Laws
negative_passages.docid: 115976
negative_passages.text: $\mathbf{Q}[\sqrt 5+\sqrt[3] 2]=\mathbf{Q}[\sqrt 5,\sqrt[3] 2]$?
negative_passages.docid: 8364
negative_passages.text: To show that Fermat number $F_{5}$ is divisible by $641$.
negative_passages.docid: 126888
negative_passages.text: How can you show that $\binom {n}{7}=\sum_{k=7}^n \binom {k-1} {6}$?
negative_passages.docid: 134885
negative_passages.text: proving that $\mathbb{Q}(\sqrt{5}, \sqrt{6}) = \mathbb{Q}(\sqrt{5}+ \sqrt{6}) $
negative_passages.docid: 105442
negative_passages.text: Show that any prime divisor of $x^4+x^3+x^2+x+1$, with $x\in\mathbb{N}$, is $5$ or $1$ mod $5$
negative_passages.docid: 7090
negative_passages.text: Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$