query: Prove that, if n is an integer and n REM 4 = 2, then is not a perfect square
positive_passages.docid: 24820
positive_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: 70386
negative_passages.text: Proof by induction: $2^n > n^2$ for all integer $n$ greater than $4$
negative_passages.docid: 26336
negative_passages.text: Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
negative_passages.docid: 135614
negative_passages.text: Show that $2^n > n^2$ whenever n>4.
negative_passages.docid: 142513
negative_passages.text: Prove that $2xy\mid x^2+y^2-x$ implies $x$ is a perfect square.
negative_passages.docid: 17047
negative_passages.text: Prove that if n is even then $n^2$ is even and if n is odd then $n^2$ is odd?
negative_passages.docid: 114873
negative_passages.text: Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
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: 23830
negative_passages.text: Proof that if $p\equiv3\,\left(\mbox{mod 4}\right)$ then $p$ can't be written as a sum of two squares
negative_passages.docid: 84220
negative_passages.text: Questions on perfect squares
negative_passages.docid: 92106
negative_passages.text: Prove that $n$ is a sum of two squares?
negative_passages.docid: 93948
negative_passages.text: Is my proof correct? $p_1p_2p_3\cdots p_n+1)$ cannot be the square of an integer
negative_passages.docid: 20964
negative_passages.text: Proof that $n^2 < 2^n$
negative_passages.docid: 148455
negative_passages.text: Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
negative_passages.docid: 33735
negative_passages.text: The square of an integer is congruent to 0 or 1 mod 4
negative_passages.docid: 59782
negative_passages.text: Are there any $n$ for which $ n^4+n^3+n^2+n+1$ is a perfect square?
negative_passages.docid: 95111
negative_passages.text: Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.