Reduce the equation modulo 7. The term 7*y^3 vanishes and 2003 is congruent to 1. Cubes modulo 7 are 0, 1, or 6, so 4*x^3 is respectively 0, 4, or 3, never 1. Hence no integers x and y satisfy the equation.
RESULT_JSON: {"modulus":7,"target_residue":1,"residue_cases":[{"x_residue":0,"x_cube_residue":0,"lhs_residue":0},{"x_residue":1,"x_cube_residue":1,"lhs_residue":4},{"x_residue":2,"x_cube_residue":1,"lhs_residue":4},{"x_residue":3,"x_cube_residue":6,"lhs_residue":3},{"x_residue":4,"x_cube_residue":1,"lhs_residue":4},{"x_residue":5,"x_cube_residue":6,"lhs_residue":3},{"x_residue":6,"x_cube_residue":6,"lhs_residue":3}]}
