query: If $a+\sqrt{a^2+1}= b+\sqrt{b^2+1}$, then $a=b$ or not?
positive_passages.docid: 142845
positive_passages.text: is $y = \sqrt{x^2 + 1}− x$ a injective (one-to-one) function?
negative_passages.docid: 73391
negative_passages.text: Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
negative_passages.docid: 33184
negative_passages.text: Something strange about $\sqrt{ 4+ \sqrt{ 4 + \sqrt{ 4-x}}}=x$ and its friends
negative_passages.docid: 68743
negative_passages.text: If $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}$ then $\frac{1}{a^5}+\frac{1}{b^5}+\frac{1}{c^5}=\frac{1}{a^5+b^5+c^5}.$
negative_passages.docid: 124097
negative_passages.text: How does += (plus equal) work?
negative_passages.docid: 71012
negative_passages.text: If $a, b$ are positive integers such that $a|b^2, b^2|a^3,....$ then $a=b$.
negative_passages.docid: 98921
negative_passages.text: Does $y(y+1) \leq (x+1)^2$ imply $y(y-1) \leq x^2$?
negative_passages.docid: 77764
negative_passages.text: Is "$a + 0i$" in every way equal to just "$a$"?
negative_passages.docid: 17532
negative_passages.text: Why does Simplify[b-a] give -a+b and not b-a?
negative_passages.docid: 100375
negative_passages.text: Prove that ${\sqrt {n} }^{\sqrt {n+1}} > {\sqrt {n+1}}^{\sqrt {n}}$.
negative_passages.docid: 131108
negative_passages.text: Can $3p^4-3p^2+1$ be square number?
negative_passages.docid: 86378
negative_passages.text: Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$
negative_passages.docid: 23406
negative_passages.text: How do I convince someone that $1+1=2$ may not necessarily be true?
negative_passages.docid: 132801
negative_passages.text: Is it true that $\lfloor\sqrt{n}+\sqrt{n+1}+\sqrt{n+2} \rfloor=\lfloor\sqrt{9n+7}\rfloor$?
negative_passages.docid: 113250
negative_passages.text: If $x+{1\over x} = r $ then what is $x^3+{1\over x^3}$?
negative_passages.docid: 11506
negative_passages.text: Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer
negative_passages.docid: 13012
negative_passages.text: Why can a = b imply 2 = 1?