Let A be the set of all polynomials f(x) of order 3 with integer coefficients and cubic coefficient 1, so that for every f(x) there exists a prime number p which does not divide 2004 and a number q which is coprime to p and 2004, so that f(p)=2004 and f(q)=0.
Prove that there exists a infinite subset BāA, so that the function graphs of the members of B are identical except of translations algebrapolynomialfunctiongeometrygeometric transformationmodular arithmeticnumber theory