query: Techniques to prove that there is only one square in a given sequence
positive_passages.docid: 22840
positive_passages.text: The sum of the first $n$ squares is a square: a system of two Pell-type-equations
negative_passages.docid: 34099
negative_passages.text: Proving that the empty set is unique
negative_passages.docid: 48430
negative_passages.text: Prove the following sequence always results in a perfect square.
negative_passages.docid: 1148
negative_passages.text: Curious limit of a sequence used to prove Etemadi's SLLN
negative_passages.docid: 35515
negative_passages.text: Find the number of $(m+n)$ digit binary sequences with $m$ $0$'s and $n$ $1$'s such that no two $1$'s are adjacent
negative_passages.docid: 141895
negative_passages.text: Proving that a sequence is monotone
negative_passages.docid: 135018
negative_passages.text: Proving that a sequence has $a_n = a_{n+2}$ for $n$ sufficiently large.
negative_passages.docid: 109920
negative_passages.text: Ordered binary sequences of length n with no two consecutive 0's without using recursion
negative_passages.docid: 41726
negative_passages.text: Musical and combinatorial proof
negative_passages.docid: 154459
negative_passages.text: Constructing a HoTT proof term of 1≠0
negative_passages.docid: 156660
negative_passages.text: The set of all strictly increasing sequences of natural numbers
negative_passages.docid: 83638
negative_passages.text: Suppose $0,0,1,0,0,1,0,0,1,...$ is a sequence. What is the general term of this sequence?
negative_passages.docid: 65168
negative_passages.text: Proof of sequence inequality
negative_passages.docid: 24820
negative_passages.text: Prove that if $n$ is a perfect square, then either $n \equiv 1 \pmod 4$, or $n \equiv 0 \pmod 4$.
negative_passages.docid: 152845
negative_passages.text: Every integer is the unique sum of a "decreasing" sequence of binomial coefficients
negative_passages.docid: 60024
negative_passages.text: Proof that a sequence is convergent
negative_passages.docid: 123357
negative_passages.text: Real Analysis - A sequence that has no convergent subsequence