query: Proving the values obtained by a recurrence relation are always perfect squares?
positive_passages.docid: 130476
positive_passages.text: Prove that every terms of a sequence defined by a recurrence relation is a perfect square.
negative_passages.docid: 18482
negative_passages.text: Can the squares with side $1/n$ be packed into a $1 \times \zeta(2)$ rectangle?
negative_passages.docid: 114810
negative_passages.text: $n!$ is never a perfect square if $n\geq2$. Is there a proof of this that doesn't use Chebyshev's theorem?
negative_passages.docid: 32350
negative_passages.text: Compilation of proofs for the summation of natural squares and cubes
negative_passages.docid: 12648
negative_passages.text: Did I correctly derive this recurrence equation formula
negative_passages.docid: 90076
negative_passages.text: Prove that every positive integer $n$ is a unique product of a square and a squarefree number
negative_passages.docid: 41641
negative_passages.text: $(n-7)(n+7)=$ some perfect square
negative_passages.docid: 135458
negative_passages.text: When is a sum of consecutive squares equal to a square?
negative_passages.docid: 83346
negative_passages.text: Finding a closed form $x_n$ for the recurrence relation $x_{n+2} = px_{n+1} + qx_n + r$
negative_passages.docid: 53244
negative_passages.text: Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$
negative_passages.docid: 72065
negative_passages.text: What is the best way to solve discrete divide and conquer recurrences?
negative_passages.docid: 93657
negative_passages.text: Proving “The sum of $n$ consecutive cubes is equal to the square of the sum of the first $n$ numbers.”
negative_passages.docid: 72666
negative_passages.text: Prime Numbers And Perfect Squares
negative_passages.docid: 86603
negative_passages.text: Infinite square-rooting
negative_passages.docid: 153692
negative_passages.text: Generating and solving recurrence relations
negative_passages.docid: 106716
negative_passages.text: The sum of square roots of non-perfect squares is never integer
negative_passages.docid: 100048
negative_passages.text: Got stuck in proving monotonic increasing of a recurrence sequence