Question 21
Consider the polynomial $p(x)=(1+x^{3^1})(1+x^{3^2})(1+x^{3^3})(1+x^{3^4})(1+x^{3^5})(1+x^{39})$. Suppose we expand the product to obtain $a_0+a_1x+a_2x^2+\cdots+a_{402}x^{402}$, where, for example, $a_0=a_{402}=1$. How many of the coefficients $a_0,\ldots,a_{402}$ are nonzero?
(A) 52
(B) 56
(C) 60
(D) 64
(E) 376
(A) 52
(B) 56
(C) 60
(D) 64
(E) 376