query: Prove or disprove: $7 \lt \sqrt{3} + \sqrt{27}$
positive_passages.docid: 117999
positive_passages.text: Prove by contradiction (not using a calculator) that $\sqrt6 + \sqrt2 < \sqrt{15}$?
negative_passages.docid: 127400
negative_passages.text: Prove that ∀ n ∈ {n | n ∈ ℕ ∧ n > 7}: n = x*3 + y*5
negative_passages.docid: 104658
negative_passages.text: proving $\csc^2 \left( \frac{\pi}{7}\right)+\csc^2 \left( \frac{2\pi}{7}\right)+\csc^2 \left( \frac{4\pi}{7}\right)=8$
negative_passages.docid: 7491
negative_passages.text: How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?
negative_passages.docid: 22058
negative_passages.text: Prove that $\cos(\pi/7)$ is root of equation $8x^3-4x^2-4x+1=0$
negative_passages.docid: 2251
negative_passages.text: Can someone give me a hint on how to prove this?
negative_passages.docid: 48053
negative_passages.text: Show that 13 divides $2^{70}+3^{70}$
negative_passages.docid: 51520
negative_passages.text: Prove that the only prime triple is 3, 5, 7
negative_passages.docid: 126074
negative_passages.text: Proof of the irrationality of $\sqrt{3}$ - logic question
negative_passages.docid: 28347
negative_passages.text: Prove that $\sqrt 2 + \sqrt 3$ is irrational
negative_passages.docid: 50777
negative_passages.text: Prove that $4\sin\frac{2\pi}{7}- \tan\frac{\pi}{7}= \sqrt{7}$ .
negative_passages.docid: 27850
negative_passages.text: Find and prove a formula for $1\pmod{3}\cap 1\pmod{7}$.
negative_passages.docid: 66016
negative_passages.text: Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$
negative_passages.docid: 21476
negative_passages.text: Modular Exponentiation 3^5^7
negative_passages.docid: 99428
negative_passages.text: Prove that $3^{2n-1} + 2^{n+1}$ is always a multiple of $7$.
negative_passages.docid: 17930
negative_passages.text: Please explain this step in proving the square root of 3 is irrational
negative_passages.docid: 23301
negative_passages.text: There does not exist any integer $m$ such that $3n^2+3n+7=m^3$