Any polynomial has a finite number of solutions – well, any? --- The non-commutative case
21743
Why are the solutions of polynomial equations so unconstrained over the quaternions?
116307
Polynomial whose only values are squares
104233
Is the ring of the polynomials on a finite algebraic set always a product of local rings?
147047
Does there exist a polynomial $p(x) \in \mathbb C[x]$ such that $p(x) \notin \mathbb R[x]$ and $p(x)p(-x)=p(x^2)$?
7085
Prove that if the equation $x^{2} \equiv a\pmod{pq}$ has any solutions, then it has four solutions.
95494
Number of solutions of an arithmetic function's equation
154487
Maximal number of monomials of multivariate polynomial
151225
Solved Problems in Algebraic Number Theory
82262
minimal polynomial of nth root of 2 over $\mathbb Q$
2408
Show that a polynomial has at least one positive solution/root.
157266
Can a nonzero polynomial evaluate to the zero function in a suitable infinite ring of char 0?
77820
Roots in a polynomial ring
131366
Cyclotomic polynomial
35664
If $x^m=e$ has at most $m$ solutions for any $m\in \mathbb{N}$, then $G$ is cyclic
109039
Does this "extension property" for polynomial rings satisfy a universal property?
54212
Another polynomial equation
82295
Showing that the minimal polynomial of an $n \times n$ matrix has degree at most $n$ without using the Cayley-Hamilton Theorem