How can I approach this question in other way without proving that $p(x)=x$ is a unique solution? $p(x^2+1)=(p(x))^2 +1$
109102
Determine all real polynomials with $P(0)=0$ and $P(x^2+1)=(P(x))^2+1$
77864
Find $P(12)$ when $P(x)={1\over(x+1)}$, for $x=0,1,2,......11$
137308
If an IVP does not enjoy uniqueness, then it possesses infinitely many solutions
13904
$p = x^2 + xy + y^2$ if and only if $p \equiv 1 \text{ mod }3$?
35874
Show that when $BA = I$, the solution of $Ax=b$ is unique
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
142584
Confusion in proof that primes $p = 4k + 1$ are uniquely the sums of two squares
109778
Proving $(x-c)|(p(x)-p(c))$
38805
Prove that $x^{2} \equiv -1 \pmod p$ has no solutions if prime $p \equiv 3 \pmod 4$.
151961
Irreducibility of $x^{p(p-1)}+x^{p(p-2)}+\cdots+x^p+1$ over $\mathbb Q$
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
91935
If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
7199
Suppose that $P(x)$ is a polynomial of degree $n$ such that $P(k)=\dfrac{k}{k+1}$ for $k=0,1,\ldots,n$. Find the value of $P(n+1)$
155757
Number theory: $x^y + 1 = y^x$
50596
$p_1p_2...p_n +1$ is not square for $p_k = k$'th prime
29811
Find all polynomials $P$ such that $P(x^2+1)=P(x)^2+1$
24837
$x^2+1=0$ uncountable many solutions