Consider the equation 3y4+4cy3+2xy+48=0, where c is an integer parameter. Determine all values of c for which the number of integral solutions (x,y) satisfying the conditions (i) and (ii) is maximal:
(i) ∣x∣ is a square of an integer;
(ii) y is a squarefree number. number theorysquarefreePerfect SquarediophantineDiophantine equation