query: $1+\sqrt{2}$ seems special: its powers quickly approach integers
positive_passages.docid: 152870
positive_passages.text: Near integers in powers of binomials with radicals
negative_passages.docid: 50555
negative_passages.text: Approximation of real number to the power of irrational
negative_passages.docid: 89716
negative_passages.text: Is there a proof of the irrationality of $\sqrt{2}$ that involves modular arithmetic?
negative_passages.docid: 125484
negative_passages.text: Fastest square number test
negative_passages.docid: 58480
negative_passages.text: Computing sums of divisors in $O(\sqrt n)$ time?
negative_passages.docid: 18932
negative_passages.text: Squares in arithmetic progression
negative_passages.docid: 24301
negative_passages.text: Can a finite sum of square roots be an integer?
negative_passages.docid: 136318
negative_passages.text: Where does the power $2$ come from in the Pythagorean theorem?
negative_passages.docid: 37219
negative_passages.text: Quadratic Integers in $\mathbb Q[\sqrt{-5}]$
negative_passages.docid: 20486
negative_passages.text: Numbers representable as $x^2 + 2y^2$
negative_passages.docid: 101162
negative_passages.text: Square root of $2$ is irrational
negative_passages.docid: 86515
negative_passages.text: Characterization of integers which has a $2$-adic square root
negative_passages.docid: 126040
negative_passages.text: Geometric explanation of $\sqrt 2 + \sqrt 3 \approx \pi$
negative_passages.docid: 90537
negative_passages.text: Converse of Fermat's Little Theorem.
negative_passages.docid: 134348
negative_passages.text: When is $(p - 1)! + 1$ a power of $p$?
negative_passages.docid: 156510
negative_passages.text: How to compute $2^{\text{some huge power}}$
negative_passages.docid: 92166
negative_passages.text: Number of odd binomial coefficients is a power of $2$