If $P(n)$ divides $P(P(n)-2015)$, prove that $P(-2015)=0$
66423
Previous year Olympiad problem (polynomials)
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
136574
Show $g^{(n)}(0)=0$ for all $n$
24098
Prove that $a$ divides $b$ and $b$ divides $a$ if and only if $a = \pm b$
5841
Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
116363
If $P(x^5)+xQ(x^5)+x^2R(x^5)=(x^4+x^3+x^2+x+1)S(x)$ , then prove that $P(x)$ is divisible by $x-1$
66089
Using AM-GM to prove $\lim_{p\to 0}$ of the $p$-mean is equal to the GM.
67394
How to interpret $\mathbb{P}(B|A)$ when $\mathbb{P}(A) = 0$
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
80144
Prove that $x-1$ divides $x^n-1$
144819
Proving $P(n) =n^{\phi(n)} \prod\limits_{d \mid n} \left(\frac{d!}{d^d} \right)^{\mu(n/d)}$
37783
Proving that a set of 2016 natural numbers contain a non-empty set with a sum divisible by 2016
110662
Show that $P(\mathbb{N})$ is equivalent to $2^\mathbb{N}$
98871
How to prove that if a prime divides a Fermat Number then $p=k\cdot 2^{n+2}+1$?
55023
if $A$ subset of $B$ then $P(B)-P(A)=P(B\setminus A)\ge 0$
100696
Let $p$ be prime. Consider the sequence: $1, 2^2, 3^3, 4^4, 5^5, 6^6 \cdots \pmod p$. Prove the sequence is periodic with smallest period $p(p-1).$
151692
When does $2^n-1$ divide $3^n-1$?