Polynomials satisfying f(x-a)f(x)+c over finite fields
Hong-Goo Park · Bulletin of the Korean Mathematical Society · 1992
Let GF(q) be a finite field with q elements where q=p for a prime number p and a positive integer n. Consider an arbitrary function .phi. from GF(q) into GF(q). By using the Largrange's Interpolation formula for the given function .phi., .phi. can be represented by a polynomial which is congruent (mod x -x) to a unique polynomial over GF(q) with the degree and (1) f(x+a)=f(x)+c for the fixed nonzero elements a and c in GF(q).