Question 120
Find all positive integers $n$ such that there exist nonzero real numbers $a, b, c, d$ for which the polynomial
$$
(ax + b)^{1000} - (cx + d)^{1000}
$$
after expanding all brackets (and collecting terms) has exactly $n$ nonzero coefficients.
$$
(ax + b)^{1000} - (cx + d)^{1000}
$$
after expanding all brackets (and collecting terms) has exactly $n$ nonzero coefficients.