query: Find the values of $p$ and $q$
positive_passages.docid: 127183
positive_passages.text: Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$
negative_passages.docid: 31724
negative_passages.text: How prove that $q \geq b+d$ for $ad-bc = 1$ and $\frac{a}{b} > \frac{p}{q} > \frac{c}{d}$?
negative_passages.docid: 83291
negative_passages.text: Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
negative_passages.docid: 125702
negative_passages.text: There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$
negative_passages.docid: 51518
negative_passages.text: Is $\sqrt[3]{p+q\sqrt{3}}+\sqrt[3]{p-q\sqrt{3}}=n$, $(p,q,n)\in\mathbb{N} ^3$ solvable?
negative_passages.docid: 137702
negative_passages.text: How I find limit of $P_n$
negative_passages.docid: 147777
negative_passages.text: If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?
negative_passages.docid: 51019
negative_passages.text: Polynomial problem with two conditions
negative_passages.docid: 47737
negative_passages.text: Find all the possible values of $(a,b,c,d)$.
negative_passages.docid: 99146
negative_passages.text: Find $\sqrt a + \sqrt b + \sqrt c$ only in terms of $p$ .
negative_passages.docid: 147307
negative_passages.text: How to evaluate $\sum_{\gcd (p,q)=1} \frac{1}{p^2q^2}$?
negative_passages.docid: 137511
negative_passages.text: Trying to show that $\sup \{b^p:p\in Q,\;0<p<x\} = \inf\{b^q:q\in Q,\;x<q\}$
negative_passages.docid: 77864
negative_passages.text: Find $P(12)$ when $P(x)={1\over(x+1)}$, for $x=0,1,2,......11$
negative_passages.docid: 116921
negative_passages.text: Find the unique pair of real numbers $(x,y)$ that satisfy $P(x)Q(y)=28$
negative_passages.docid: 124742
negative_passages.text: P(A|C)=P(A|B)*P(B|C)?
negative_passages.docid: 79
negative_passages.text: Find $a$, $b$ and $c$ that satisfy the following equations
negative_passages.docid: 66892
negative_passages.text: Finding $P$ in $A = P^{-1}JP$ (Jordan Form)