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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
20
votes
$P(x)=P(y)$ has infinitely many integer solutions
First it is clear (assuming throughout that $P$ is a solution to your problem) that $P$ should have even degree, for if $P$ has odd degree we have $\lim\limits_{n \rightarrow -\infty}P(n) = -\infty$ a …
1
vote
Combinatorics- Equal partitions
Solutions to USAMO problems can be found online. See this link: https://mks.mff.cuni.cz/kalva/usa/usoln/usol865.html