query: Prove that a number all of whose digits are either $6$ or $0$ cannot be a perfect square
positive_passages.docid: 24601
positive_passages.text: Proving that a natural number made entirely of 6's and 0's is not a square.
negative_passages.docid: 114542
negative_passages.text: Can a number with $100$ $0$'s $100$ $1$'s and $100$ $2$'s ever be a perfect square?
negative_passages.docid: 72437
negative_passages.text: Sum of the digits of a perfect square
negative_passages.docid: 134377
negative_passages.text: The minimum number of digits after the floating-point, which uniquely identify every irrational square root
negative_passages.docid: 22800
negative_passages.text: Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
negative_passages.docid: 12365
negative_passages.text: Show that every prime $p>3$ is either of the form $6n+1$ or of the form $6n+5$
negative_passages.docid: 72666
negative_passages.text: Prime Numbers And Perfect Squares
negative_passages.docid: 99037
negative_passages.text: Prove the sum of all numbers that do not have a multiplicative inverse mod $n$
negative_passages.docid: 121469
negative_passages.text: Proof of observations on natural numbers being expressed as differences of squares.
negative_passages.docid: 145558
negative_passages.text: Prove that $2^n+3^n $ is never a perfect square
negative_passages.docid: 99606
negative_passages.text: Prove or disprove there exists a set of four numbers out of the $48$ positive integers of which product is a perfect square
negative_passages.docid: 118538
negative_passages.text: Find all integers $x$ such that $x^2+3x+24$ is a perfect square.
negative_passages.docid: 28099
negative_passages.text: Proving any number of the form $2^n$ can't be written as the sum of k consecutive numbers.
negative_passages.docid: 136366
negative_passages.text: Show that if $2+2\sqrt{28n^2+1}$ is an integer then it must be perfect square.
negative_passages.docid: 38498
negative_passages.text: Find all primes $p$ such that $(2^{p-1}-1)/p$ is a perfect square
negative_passages.docid: 48430
negative_passages.text: Prove the following sequence always results in a perfect square.
negative_passages.docid: 90076
negative_passages.text: Prove that every positive integer $n$ is a unique product of a square and a squarefree number