A problem in polynomials to show there are polynomials $f_{1}(x), \cdots f_{k}(x)$ such that $ P(x) = \sum_{j = 1}^{k} (f_{j} (x))^{2}$
53244
Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
47443
Iterated polynomial problem
56311
Proving $(1+a_{2})^{2}(1+a_{3})^{3}\cdots(1+a_{n})^{n}\ge n^n$ for positive reals $a_2,\ldots, a_n$ whose product is $1$
101057
Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
127547
Prove that If $f$ is polynomial function of even degree $n$ with always $f\geq0$ then $f+f'+f''+\cdots+f^{(n)}\geq 0$.
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
33903
Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
65901
Solution verification to complex analysis problem, prove $f$ is a polynomial.
80397
Show that this set of polynomials is ideal in F[x]
89354
Polynomials, prove exercise question about question
142360
How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$
132410
Difficult Polynomial Question
25961
Prove: $\binom{n}{0}F_0+\binom{n}{1}F_1+\binom{n}{2}F_2+\cdots+\binom{n}{n}F_n=F_{2n}$
129834
Show that there is a unique polynomial of degree at most $2n+1$ such that $q^{[k]}(x_1)=a_k,$ $q^{[k]}(x_2)=b_k$ for $k=0, \dots, n$.
62254
Show $F_{n+1} \cdot F_{n-1} = F_n^2 + (-1)^n$ for all $n \in \mathbb{N}$
154373
How many irreducible monic quadratic polynomials are there in $\mathbb{F}_p[X]$?