For every function f: Fp -> Fp, where p is prime, there exists a polynomial Q of degree at most p-1 such that f(x) = Q(x) for all x in Fp. The discussion raises questions about the applicability of polynomial interpolation in finite fields, with some participants expressing confusion about the concept of interpolation in this context. It is noted that polynomial interpolation can work over any field, but the finite nature of Fp complicates the idea of finding values between given values. Participants clarify that while a polynomial of degree p-1 has p coefficients, the connection to the function f remains unclear for some. The conversation emphasizes the need for a deeper understanding of polynomial behavior in finite fields.