Conservative definition
Parameters: n, s
((exists bcs_sqrt_lower_gap_bertrand_defined_floor_sqrt. bcs_sqrt_lower_gap_bertrand_defined_floor_sqrt + (s) * (s) = (n)) /\ exists bcs_sqrt_upper_gap_bertrand_defined_floor_sqrt. bcs_sqrt_upper_gap_bertrand_defined_floor_sqrt + S (n) = S (s) * S (s))