MathDB

A polynomial product of the form

(1-z)^{b_1}(1-z^2)^{b_2}(1-z^3)^{b_3}(1-z^4)^{b_4}(1-z^5)^{b_5}\cdots(1-z^{32})^{b_{32}},

where the

b_k

are positive integers, has the surprising property that if we multiply it out and discard all terms involving

z

to a power larger than

32

, what is left is just

1-2z

. Determine, with proof,

b_{32}

Problem Statement