query: Give two integers $m$ and $n$ such that $n^2$ is a multiple of $m$, $n$ is not a multiple of $m$ and $n > m$
positive_passages.docid: 153100
positive_passages.text: A counterexample to "$k\mid n$ if and only if $k\mid n^2$"
negative_passages.docid: 47060
negative_passages.text: Split $n$ into nontrivial factors via a nontrivial square-root of $1\!\pmod{\!n}$
negative_passages.docid: 141531
negative_passages.text: Find the set of $n\in\Bbb Z^+$ with $M=\{n,n+1,n+2,n+3,n+4,n+5\}$ partitionable into two sets
negative_passages.docid: 88982
negative_passages.text: Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
negative_passages.docid: 49427
negative_passages.text: $l^2+m^2=n^2$ $\implies$ $lm$ is always a multiple of 3 when $l,m,n,$ are positive integers.
negative_passages.docid: 76032
negative_passages.text: Prove that if m is a square integer then m is neither congruent to 2 modulo 5 nor congruent to 3 modulo 5
negative_passages.docid: 20964
negative_passages.text: Proof that $n^2 < 2^n$
negative_passages.docid: 40626
negative_passages.text: Suppose that $ a,b \in \mathbb{Z}$ If 4 divides $ a^2 + b^2$, then $a$ and $b$ are not odd.
negative_passages.docid: 72389
negative_passages.text: Positive integer $n$ such that $2n+1$ , $3n+1$ are both perfect squares
negative_passages.docid: 103784
negative_passages.text: Show that $n^2+11n+2$ is not divisible by $113^2$ ( n is integer)
negative_passages.docid: 112575
negative_passages.text: Finding integer solutions of $m^2-n^5 = m - n$
negative_passages.docid: 77806
negative_passages.text: Proving if $a$ is not a multiple of prime $p$, then an integer $b$ exists such that $p^b - 1$ is a multiple of $a$
negative_passages.docid: 36011
negative_passages.text: Show that the product of two consecutive natural numbers is never a square.
negative_passages.docid: 135241
negative_passages.text: Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group
negative_passages.docid: 156577
negative_passages.text: The cube of any number not a multiple of $7$, will equal one more or one less than a multiple of $7$
negative_passages.docid: 70006
negative_passages.text: $a,b,m,n$ be positive integers such that g.c.d.$(a,b)=1$ and $a^m+b^m|a^n+b^n$ , then $m|n$?
negative_passages.docid: 40565
negative_passages.text: How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$