query: Find all functions such that $f(m)+f(n)|m^p+n^p$
positive_passages.docid: 144473
positive_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 $
negative_passages.docid: 41876
negative_passages.text: Finding an asymptotic for the sum $\sum_{p\leq x}p^m$
negative_passages.docid: 73519
negative_passages.text: Determine all functions satisfying $f(x + f(x + y)) + f(xy) = x + f(x + y) +yf(x)$
negative_passages.docid: 140462
negative_passages.text: Find a closed form for the power series $f_p(x)=\sum\limits_{n=0}^\infty\frac{n^p}{n!}x^n$
negative_passages.docid: 155575
negative_passages.text: Proving a polynomial $f(x)$ composite for infinitely many $x$
negative_passages.docid: 90261
negative_passages.text: Find all solutions of the equation $n^m=x^2+py^2$ which satisfy the following properties
negative_passages.docid: 143466
negative_passages.text: Roots of functions / polynomials
negative_passages.docid: 53745
negative_passages.text: Euler's $\phi$ function: Find all $n$ such that $\phi(n)=n/3$
negative_passages.docid: 31698
negative_passages.text: $f(m^2 + f(n)) = f(m)^2 + n$ for all natural numbers
negative_passages.docid: 122519
negative_passages.text: Multiplicative Functions
negative_passages.docid: 46065
negative_passages.text: How do you find all $n$ such that $\phi(n)|n$
negative_passages.docid: 113740
negative_passages.text: Find a uniformly continuous function such that $a_{n+1}=f(a_n)$
negative_passages.docid: 106748
negative_passages.text: Number of functions $f : A \to A$ such that $f(f(x))=f(x)$
negative_passages.docid: 86128
negative_passages.text: Find all functions $ f : \Bbb R \to \Bbb R$ which satisfy $f(x)f(y) = f(x + y) + xy$ for all $x, y ∈ \Bbb R$.
negative_passages.docid: 41810
negative_passages.text: Should all polynomial functions from F to F (F is a field) have coefficients in F?
negative_passages.docid: 33099
negative_passages.text: If $f$ is an entire function where every power series expansion has at least one 0 term, show it is a polynomial
negative_passages.docid: 151947
negative_passages.text: Finding a pair of functions with properties