query: Show that $3n^4+3n^2+1$ is never a perfect square
positive_passages.docid: 153377
positive_passages.text: How to solve $y^2=3x^4+3x^2+1$ for integers.
negative_passages.docid: 54355
negative_passages.text: $1+x+\ldots+x^n$ perfect square
negative_passages.docid: 94019
negative_passages.text: Find all $p$'s such that $p^4 + p^3 + p^2 + p +1$ is a perfect square.
negative_passages.docid: 57639
negative_passages.text: Show there exists an $\alpha\in F_{p^n}$ such that $\alpha +\alpha^p+\alpha^{p^2}+\cdots+\alpha^{p^{n-1}}\neq 0$
negative_passages.docid: 8034
negative_passages.text: Can $n!$ be a perfect square when $n$ is an integer greater than $1$?
negative_passages.docid: 147666
negative_passages.text: How to prove that either $2^{500} + 15$ or $2^{500} + 16$ isn't a perfect square?
negative_passages.docid: 152643
negative_passages.text: $(xy + 1)(yz + 1)(zx + 1) $ is a perfect square if and only if each factor is
negative_passages.docid: 86285
negative_passages.text: Given positive integers $ x , y$ and that $3x^2 + x = 4y^2 +y$ Prove that $x-y$ is a perfect square
negative_passages.docid: 69902
negative_passages.text: $3$ never divides $n^2+1$
negative_passages.docid: 45911
negative_passages.text: Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer
negative_passages.docid: 68561
negative_passages.text: How to show $\lceil ( \sqrt3 +1)^{2n}\rceil$ where $n \in \mathbb{ N}$ is divisible by $2^{n+1}$
negative_passages.docid: 152754
negative_passages.text: When is the sum of divisors a perfect square?
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: 19588
negative_passages.text: $n!+1$ being a perfect square
negative_passages.docid: 22973
negative_passages.text: Show that an integer of the form $8k + 7$ cannot be written as the sum of three squares.
negative_passages.docid: 78593
negative_passages.text: Prove that the product of four consecutive positive integers plus one is a perfect square
negative_passages.docid: 44307
negative_passages.text: Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$