This is my hypothesis and I am not sure if this is a valid one. I need a proof for this. My point is that infinite number of minimas are needed if this is valid, but I am lack of knowledge to prove it.
Any one has a proof ?
Hypotehis:
I want to show that a non-constant polynomial $P(x)$ where $x \in \mathbb{N}$ can not have infinite number of the same constant values in its range.
i.e. for some infinite set of distinct $x_i$ values, where $i \in \mathbb{N}$ and $c$ is a constant, $P(x_i) \ne c $