query: Why $p_1\mid a \wedge p_2\mid a \Rightarrow p_1p_2\mid a$?
positive_passages.docid: 20881
positive_passages.text: Prove that if $p$ and $q$ are distinct primes such that $pq\mid n^2$ then $pq\mid n$.
negative_passages.docid: 61066
negative_passages.text: Prove: $(A\rightarrow B),(A\rightarrow C)\rightarrow B, \mapsto_{HPC} B $
negative_passages.docid: 95513
negative_passages.text: Proving $W$ is a subspace of $P_{2}$
negative_passages.docid: 80421
negative_passages.text: Show that $a - b \mid f(a) - f(b)$
negative_passages.docid: 25260
negative_passages.text: Extension of a morphism $k^*\rightarrow X$ to $\mathbb{P}^1\rightarrow \overline{X}$
negative_passages.docid: 78463
negative_passages.text: Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$
negative_passages.docid: 35236
negative_passages.text: Proof $p \vdash q \Rightarrow p$
negative_passages.docid: 148458
negative_passages.text: $x^p-x \equiv x(x-1)(x-2)\cdots (x-(p-1))\,\pmod{\!p}$
negative_passages.docid: 153869
negative_passages.text: Under what $p$, $-1$ is a square in $\mathbf F_p$?
negative_passages.docid: 40848
negative_passages.text: $a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
negative_passages.docid: 67709
negative_passages.text: Stuck with proof for $\forall A\forall B(\mathcal{P}(A)\cup\mathcal{P}(B)=\mathcal{P}(A\cup B)\rightarrow A\subseteq B \vee B\subseteq A)$
negative_passages.docid: 91935
negative_passages.text: If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
negative_passages.docid: 114254
negative_passages.text: Zero divisors in $A[x_1,x_2,\dots,x_r]$
negative_passages.docid: 76100
negative_passages.text: Showing that $\left\langle a,b \mid abab^{-1}\right\rangle \cong \pi_1(K) \cong \left\langle c,d \mid c^2 d^2 \right\rangle$
negative_passages.docid: 134384
negative_passages.text: What does $\rightarrow$ mean in $p \rightarrow q$
negative_passages.docid: 11693
negative_passages.text: If $p \mid m^p+n^p$ prove $p^2 \mid m^p+n^p$
negative_passages.docid: 6098
negative_passages.text: Let $f:A\rightarrow B$ and $C\subset B,D\subset B$. Prove that $f^{-1}(C\backslash D)=f^{-1}(C)\backslash f^{-1}(D)$