This problem is about polynomials with coefficients in GF(q) for some prime q E N. We say that two such polynomials f and g are equivalent if f (x) = g(x) for every x E GF(q). (a) Use Fermat's Little Theorem to find a polynomial with degree strictly less than 5 that is equiv- alent to f(x) = x over GF(5); then find a polynomial with degree strictly less than 11 that is equivalent to g(x) = 1+ 3xll + 7x13 over GF(11). (b) Prove that whenever f (x) has degree > q, it is equivalent to some polynomial f(x) with degree <