# Questions tagged [polynomials]

Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.

**345**

**15**answers

### Why do roots of polynomials tend to have absolute value close to 1?

**246**

**7**answers

### Polynomial representing all nonnegative integers

**179**

**10**answers

### If $f$ is infinitely differentiable then $f$ coincides with a polynomial

**87**

**11**answers

### Can a non-surjective polynomial map from an infinite field to itself miss only finitely many points?

**70**

**7**answers

### Roots of truncations of $ e^x - 1$

**61**

**6**answers

### How to recognise that the polynomial method might work

**56**

**4**answers

### Degree of sum of algebraic numbers

**55**

**9**answers

### Irreducibility of polynomials in two variables

**51**

**5**answers

### Bizarre operation on polynomials

**50**

**6**answers

### Why does $d^n \exp(-x-x^{-1})/(dx)^n$ only have $n$ positive real zeroes?

**47**

**2**answers

### Polynomials having a common root with their derivatives

**47**

**2**answers

### Does one real radical root imply they all are?

**46**

**2**answers

### Polynomial with the primes as coefficients irreducible?

**46**

**1**answer

### How to prove this polynomial always has integer values at all integers?

**42**

**4**answers

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

**41**

**5**answers

### The resultant and the ideal generated by two polynomials in $\mathbb{Z}[x]$

**41**

**4**answers

### Polynomial roots and convexity

**38**

**5**answers

### Which polynomial's roots are its coefficients?

**37**

**4**answers

### The sum of squared logarithms conjecture

**36**

**2**answers

### A question on maps from $\mathbb{Z}/p\mathbb{Z}$ to itself

**36**

**2**answers

### A curious identity related to finite fields

**35**

**4**answers

### Generalizing the notion of Farey neighbors to the algebraic numbers

**33**

**7**answers

### On the polynomial $\sum_{k=0}^n\binom{n}{k}(-1)^kX^{k(n-k)}$

**32**

**12**answers

### What Are Some Naturally-Occurring High-Degree Polynomials?

**32**

**4**answers

### A family of polynomials whose zeros all lie on the unit circle

**31**

**3**answers

### Polynomials with the same values set on the unit circle

**31**

**1**answer

### Integers not represented by $ 2 x^2 + x y + 3 y^2 + z^3 - z $

**31**

**3**answers

### Are surjectivity and injectivity of polynomial functions from $\mathbb{Q}^n$ to $\mathbb{Q}$ algorithmically decidable?

**31**

**1**answer

### Finding a path through real rooted polynomials

**29**

**2**answers

### Polynomial $g:\mathbb R^n \rightarrow\mathbb R^n$ with no critical point may have no root

**29**

**1**answer

### Zeros of polynomials with real positive coefficients

**28**

**3**answers

### Is $x^{2k+1} - 7x^2 + 1$ irreducible?

**28**

**6**answers

### Bass' stable range of $\mathbf Z[X]$

**28**

**3**answers

### when is the power of a nonnegative polynomial a sum of squares?

**28**

**1**answer

### Polynomials non-negative on the integers

**27**

**12**answers

### When does 'positive' imply 'sum of squares'?

**27**

**1**answer

### How many polynomial Morse functions on the sphere?

**26**

**5**answers

### Given a polynomial f, can there be more than one constant c such that every root of f(x)-c is repeated?

**26**

**3**answers

### All polynomials are the sum of three others, each of which has only real roots

**25**

**4**answers

### Distribution of roots of complex polynomials

**25**

**7**answers

### When is a monic integer polynomial the characteristic polynomial of a non-negative integer matrix?

**25**

**4**answers

### $\binom{x}{2}+\binom{x}{4}+\cdots+\binom{x}{2u}$ is a convex function on $[0,+\infty)$?

**25**

**2**answers

### Are there irreducible polynomials with all zeros on two concentric circles?

**25**

**2**answers

### Are these two new ways of representing odd zeta values as integrals known?

**25**

**0**answers

### Mathieu group $M_{23}$ as an algebraic group via additive polynomials

**24**

**4**answers

### How did Ramanujan discover this identity?

**24**

**1**answer

### $f(x)$ is irreducible but $f(x^n)$ is reducible

**24**

**3**answers

### Changing the signs of the coefficients of a polynomial to make all the roots real

**23**

**5**answers

### Monic polynomial with integer coefficients with roots on unit circle, not roots of unity?

**23**

**5**answers