query: Functions such that $f(f(n))=n+2015$
positive_passages.docid: 28927
positive_passages.text: IMO 1987 - function such that $f(f(n))=n+1987$
negative_passages.docid: 409
negative_passages.text: functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
negative_passages.docid: 83036
negative_passages.text: f(g(x)) has a degree divisible by n
negative_passages.docid: 28011
negative_passages.text: Does there exists an entire function such that for each $|z|>C$ for some constant $C$, $|f(z)|=|z|+1$?
negative_passages.docid: 25563
negative_passages.text: Count number of increasing functions, nondecreasing functions $f: \{1, 2, 3, \ldots, n\} \to \{1, 2, 3, \ldots, m\}$, with $m \geq n$.
negative_passages.docid: 44238
negative_passages.text: Let $f: \mathbb N \rightarrow \mathbb N$ are increasing function such that $f\left(f(n)\right)=3n$. Find $f(2017)$
negative_passages.docid: 144222
negative_passages.text: If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
negative_passages.docid: 132488
negative_passages.text: Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$
negative_passages.docid: 111756
negative_passages.text: How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
negative_passages.docid: 107659
negative_passages.text: Let $f:A \to B$ and $g:B\to A$ be arbitrary functions.
negative_passages.docid: 31698
negative_passages.text: $f(m^2 + f(n)) = f(m)^2 + n$ for all natural numbers
negative_passages.docid: 144445
negative_passages.text: Functions $f:\mathbb{N}\rightarrow \mathbb{Z}$ such that $\left(m-n\right) \mid \left(f(m)-f(n)\right)$
negative_passages.docid: 44293
negative_passages.text: Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
negative_passages.docid: 56827
negative_passages.text: Functions that are their Own nth Derivatives for Real $n$
negative_passages.docid: 148774
negative_passages.text: show elements of order 15 in $S_8$ satisfy a relation
negative_passages.docid: 113740
negative_passages.text: Find a uniformly continuous function such that $a_{n+1}=f(a_n)$
negative_passages.docid: 153510
negative_passages.text: Questions about the existence of a function