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An arithmetic progression is a (possibly infinite) sequence of numbers such that the difference between consecutive terms is always the same value.
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Arithmetic progressions inside polynomial sets
I think I have a proof, given by a friend of mine. I’m going to post the proof when the degree is 3, but it is easy to do a generalization.
Assume $p(x)=ax^3+bx^2+cx$, and for all $i\in\{0,1,2,3\}$ w …