query: Find all the numbers $n$ such that $\frac{6n-8}{2n-5}$ can't be reduced.
positive_passages.docid: 16537
positive_passages.text: Find all the numbers $n$ such that $\frac{4n-5}{60-12n}$ can't be reduced.
negative_passages.docid: 92554
negative_passages.text: How many lattice paths are there from $(0,0)$ to $(2n,2n)$ that avoids odd points
negative_passages.docid: 39199
negative_passages.text: closed form for $\binom{n}{0}+\binom{n}{3}+\binom{n}{6}+...+\binom{n}{n}$
negative_passages.docid: 15268
negative_passages.text: Find all $x,y \in \mathbb N^*$ such that $\frac{1}{x} + \frac{1}{y}=5$
negative_passages.docid: 72511
negative_passages.text: If $n$ is an odd natural number, then $8$ divides $n^{2}-1$
negative_passages.docid: 39716
negative_passages.text: Prove that $8(5)^n + 6(3)^{2n} - 80n - 14$ is divisible by $512$ for all $n \in \mathbb{N}$ by induction.
negative_passages.docid: 98963
negative_passages.text: Prove that neither $A$ nor $B$ is divisible by $5$
negative_passages.docid: 28099
negative_passages.text: Proving any number of the form $2^n$ can't be written as the sum of k consecutive numbers.
negative_passages.docid: 44409
negative_passages.text: Number of Elements Not divisble by 3 or 5 or 7
negative_passages.docid: 124816
negative_passages.text: Using the fact that $n^3 + 5n$ is divisible by $6$, infer that $n^4 - 2n^3 + 11n^2 + 14n$ is always divisible by $24$
negative_passages.docid: 92772
negative_passages.text: How many different sets of $6$ different numbers can we construct from $11, 13, 18, 19, 19, 20, 23, 25$?
negative_passages.docid: 3611
negative_passages.text: How to prove $n^5 - n$ is divisible by $30$ without reduction
negative_passages.docid: 134454
negative_passages.text: Proof that every number ≥ $8$ can be represented by a sum of fives and threes.
negative_passages.docid: 33866
negative_passages.text: Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
negative_passages.docid: 110383
negative_passages.text: How many numbers less than $m$ and relatively prime to $n$, where $m>n$?
negative_passages.docid: 98082
negative_passages.text: Another combinatorics problem: $\sum\limits_{k = 0}^n (-1)^k \binom{2n-k}k2^{2n-2k}=2n+1$
negative_passages.docid: 53156
negative_passages.text: Infinitely many numbers not expressible in the form $a^n+b^n+c^n$