Prove that there is no polynomial with integer coefficients such that $p(a)=b,\,p(b)=c,\,p(c)=a$ for distinct integers $a,b,c$
1962
Polynomial $P(a)=b,P(b)=c,P(c)=a$
42265
A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial
6332
If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined
147952
Why can we prove mathematically that a formula to solve an (n+5) order polynomial does not exist?
99000
No polynomial with integer coefficients satisfies the conditions
40014
A polynomial that is zero on an open set
120627
Reducibility of polynomials modulo p
114812
Let $p(z)=z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+...+a_0$ be a complex polynomial satisfying $|p(z)| \leq 1$ for $|z|\leq 1$, then prove that $p(z)=z^n$
55119
Proof that the coefficients of a polynomial are real
155559
Quickest way to determine a polynomial with positive integer coefficients
47792
Integer coefficient polynomial - values as powers of 2
29811
Find all polynomials $P$ such that $P(x^2+1)=P(x)^2+1$
77620
Irreducible polynomials over $\mathbb Q$ and $\mathbb Z $
38419
Existence of Polynomial with whom product contains only prime powers
157487
Showing a polynomial having at least one integer root under certain conditions has precisely one integer root
43511
Proving products of coefficients of two polynomials are zero when the product of the polynomials is zero
13083
If for a polynomial $P(k) = 2^k$ for $k = 0, 1, . . . , n$, what is $P(n+1)$?