Let $a$, $b$ and $c$ be three distinct integers and $P$ a polynomial with integer coefficients. Show: $P(a)=b, P(b)=c$ and $P(c)=a$ isn't possible
4885
Polynomials with integer coefficients such that $p(a)=b,p(b)=c,p(c)=a$
24499
Finding $(a, b, c)$ with $ab-c$, $bc-a$, and $ca-b$ being powers of $2$
139930
Find all polynomials $p$ such that $p(x^2)=p(x)p(x+1)$
140412
If $p$ and $q$ are distinct primes such that $p|c$ and $q|c$, prove that $pq|c$
128387
Given that $a+b\sqrt[3]{2} +c\sqrt[3]{4} =0$, where $a,b,c$ are integers. Show $a=b=c=0$
29811
Find all polynomials $P$ such that $P(x^2+1)=P(x)^2+1$
6332
If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined
139082
If $a,b,c>0$ and $a^3+b^3=c^3$ then prove that $a^2+b^2-c^2>6(c-a)(c-b)$.
53244
Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$
53139
How to demonstrate that there is no all-prime generating polynomial with rational cofficents?
110464
Let $A=\{1,...,n\}.$ Show that there is a bijection of $P(A)$ with the cartesian product $X^n$ where $X$ is the two element set $X=\{0,1\}$
135768
Find $P(n+1)$ for a polynomial P
93948
Is my proof correct? $p_1p_2p_3\cdots p_n+1)$ cannot be the square of an integer
25290
Determine the number of irreducible monic polynomials of degree 3 in $\mathbb F_p[x]$
68528
$f(x)=x^n+5x^{n-1}+3$ can't be expressed as the product of two polynomials
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
39346
Let $R= \mathbb{Q}[x^2 ,x^3 ]$, the set of all polynomials over $\mathbb{Q}$ with no $x$ term. Show that the $\gcd$ of $x^5$ and $x^6$ does not exist