query: Is this an acceptable proof for If $d^{2}\mid a^{2}$ , then $d\mid a$?
positive_passages.docid: 10236
positive_passages.text: Show that $a^n \mid b^n$ implies $a \mid b$
negative_passages.docid: 18140
negative_passages.text: When does $\,n\mid q^3 \Rightarrow n\mid q\,$?
negative_passages.docid: 34714
negative_passages.text: What is the relationship between $\ker(A), \ker(A^2), \ldots, \ker(A^n)$?
negative_passages.docid: 95588
negative_passages.text: Prove by Contradiction: if $4\mid a^2 + b^2$, then $a$ and $b$ are not both odd
negative_passages.docid: 149634
negative_passages.text: $ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$
negative_passages.docid: 114867
negative_passages.text: Prove $\forall n\geq 2,n\in\mathbb{Z}$, $(n+1)\mid(n^3+1)$
negative_passages.docid: 136304
negative_passages.text: Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
negative_passages.docid: 70620
negative_passages.text: From $n=2$ to $n$-ary Euclid lemma $\ p\mid a_1\cdots a_n\Rightarrow\ p\mid a_1\,$ or $\,\cdots\, p\mid a_n$
negative_passages.docid: 153100
negative_passages.text: A counterexample to "$k\mid n$ if and only if $k\mid n^2$"
negative_passages.docid: 118574
negative_passages.text: prove that $24 \mid a(a^2-1)$
negative_passages.docid: 78463
negative_passages.text: Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$
negative_passages.docid: 35948
negative_passages.text: How to prove $D^n/S^{n-1}\cong S^n$?
negative_passages.docid: 22845
negative_passages.text: Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
negative_passages.docid: 12100
negative_passages.text: $n \mid (a^{n}-b^{n}) \ \Longrightarrow$ $n \mid \frac{a^{n}-b^{n}}{a-b}$
negative_passages.docid: 147902
negative_passages.text: Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$
negative_passages.docid: 90916
negative_passages.text: Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
negative_passages.docid: 145041
negative_passages.text: Given that $p$ is a prime and $p\mid a^n$, prove that $p^n\mid a^n$.