Let's say I have a finite field $A$, and I choose $N$ (distinct) points uniformly at random from $A \times A$. Then using Lagrange interpolation I can find a polynomial $f(x)$ of degree $N-1$ that goes through all my points. Is $f$ a random polynomial? That is, are its coefficients also uniform at random?
2026-03-25 06:08:51.1774418931
$N$ random points make a random polynomial?
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