query: Can there exist two different prime numbers, such that their roots added together equal a rational number?
positive_passages.docid: 6869
positive_passages.text: The square roots of different primes are linearly independent over the field of rationals
negative_passages.docid: 96647
negative_passages.text: Number theory: Problem involving rational numbers
negative_passages.docid: 63409
negative_passages.text: If $x^2+ax+b=0$ has a rational root, show that it is in fact an integer
negative_passages.docid: 9787
negative_passages.text: Primitive roots modulo primes congruent to n!
negative_passages.docid: 45454
negative_passages.text: Pairs of $(p,q)$ such that $p^2 + 1 = 2 q^2$?
negative_passages.docid: 132928
negative_passages.text: Digits of $\pi$ forming primes?
negative_passages.docid: 143054
negative_passages.text: Can you raise $\pi$ to a real power to make it rational?
negative_passages.docid: 5142
negative_passages.text: Infinitely many primes of the form $pn+1$
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: 2321
negative_passages.text: Can there be two distinct, continuous functions that are equal at all rationals?
negative_passages.docid: 44250
negative_passages.text: rational number solutions to $\frac{a}{a^2+1} + \frac{b}{b^2+1} = \frac{c}{c^2+1}$ with $abc\ne 0$
negative_passages.docid: 107765
negative_passages.text: Prove that there exists two roots in $[-1,1]$
negative_passages.docid: 103323
negative_passages.text: Finding a primitive root of a prime number
negative_passages.docid: 98468
negative_passages.text: Are there infinitely many primes of the form $n!+1$?
negative_passages.docid: 152172
negative_passages.text: Does there exist a positive irrational number $\alpha $, such that for any positive integer $n$ the number $\lfloor n\alpha \rfloor$ is not a prime?
negative_passages.docid: 9043
negative_passages.text: finding infinetely many primes in three different forms of prime numbers below
negative_passages.docid: 117132
negative_passages.text: Rationals of the form $\frac{p}{q}$ where $p,q$ are primes in $[a,b]$