query: Let $f: \mathbb N \rightarrow \mathbb N$ are increasing function such that $f\left(f(n)\right)=3n$. Find $f(2017)$
positive_passages.docid: 147195
positive_passages.text: Help needed in finding the value of $f(2001)$ in the given functional equation
negative_passages.docid: 52858
negative_passages.text: Find $f$ if $ f(x)+f\left(\frac{1}{1-x}\right)=x $
negative_passages.docid: 135606
negative_passages.text: No function $f:\mathbb{Z}\rightarrow \{1, 2, 3\}$ satisfying $f(x)\ne f(y)$ for all integers $x,y$ and $|x-y|\in\{2, 3, 5\}$
negative_passages.docid: 82222
negative_passages.text: Determine the number of functions $f: \{1,2,3....,1999\}\to \{2000,2001,2002,2003\}$satisfying the condition that $f(1)+f(2)+...f(1999)$ is odd.
negative_passages.docid: 48891
negative_passages.text: Show that: lim$_{n\rightarrow \infty}\,f(x_n)=f(\text{lim}_{n \rightarrow \infty} \, x_n)$
negative_passages.docid: 55286
negative_passages.text: Functional equation: $f: \mathbb{R} \rightarrow \mathbb{R}$, $f((x + 1) f(y)) = y (f(x) + 1)$
negative_passages.docid: 32432
negative_passages.text: Strategies to find the set of functions $f:\mathbb R\to\mathbb R$ satisfing the functional equation: $f(x^3)+f(y^3)=(x+y)(f(x^2)+f(y^2)-f(xy))$
negative_passages.docid: 83080
negative_passages.text: Question regarding $f(n)=\cot^2\left(\frac\pi n\right)+\cot^2\left(\frac{2\pi}n\right)+\cdots+\cot^2\left(\frac{(n-1)\pi}n\right)$
negative_passages.docid: 69734
negative_passages.text: how to find all functions such that $f\left( x^{2} - y^{2} \right) = ( x - y )( f(x) + f(y) )$
negative_passages.docid: 91947
negative_passages.text: Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
negative_passages.docid: 44293
negative_passages.text: Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
negative_passages.docid: 20199
negative_passages.text: Find a surjective function $f:\mathbb{N}\to \mathbb{Q}$
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: 14495
negative_passages.text: I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$
negative_passages.docid: 138026
negative_passages.text: To show that $n!f(x) \in \mathbb{Z}[x]$
negative_passages.docid: 61670
negative_passages.text: Proving that $(b_n) \to b$ implies $\left(\frac{1}{b_n}\right) \to \frac{1}{b}$
negative_passages.docid: 144473
negative_passages.text: Finding all functions $ f : \mathbb N^*\to\mathbb N^*$ such that for every $ x , y \in \mathbb N ^ * $, $ f ( x ) + f ( y ) \mid x ^ n + y ^ n $