# Tagged Questions

**6**

votes

**0**answers

355 views

### How many values a polynomial map misses?

Let $F$ be a field. For a uni-variate polynomial $f(x)$ over $F$,let $M_f(F)$ denote the number of values that $f$ misses, that is, the cardinality of the subset $F - f(F)$ in $F$. Assume that $f$ is ...

**34**

votes

**4**answers

2k views

### The maximum of a polynomial on the unit circle

Encouraged by the progress made in a recently posted MO problem, here is a "conceptually related" problem originating from a 2003 joint paper of Sergei Konyagin and myself.
Suppose we are given $n$ ...

**0**

votes

**1**answer

347 views

### Something new in old question about sums of three polynomial cubes ?

An old problem asks whether or not the polynomial
$$
t \in \mathbb{Q}[t]
$$
is a sum of three cubes, (of polynomials in $\mathbb{Q}[t]$).
Question: Something new known now ?
Somebody has an idea of ...

**42**

votes

**2**answers

3k views

### Polynomials having a common root with their derivatives

Here is a question someone asked me a couple of years ago. I remember having spent a day or two thinking about it but did not manage to solve it. This may be an open problem, in which case I'd be ...

**9**

votes

**0**answers

697 views

### Dissecting trapezoids into triangles of equal area

[Lightly edited for copy and proper formatting of mathematics. -- Pete L. Clark]
The Background: Let $T$ be a trapezoid. Sherman Stein, using valuation theory, showed that if $T$ is dissectible into ...

**9**

votes

**5**answers

2k views

### On Polynomials dividing Exponentials

EDIT: it turns out that no answer to this is known, as the authors of the book it is in have now confirmed they do not know how to do it. Will Jagy.
ORIGINAL: I have been wondering if there exist ...