USAMO
1988
A polynomial product of the form (1−z)b1(1−z2)b2(1−z3)b3(1−z4)b4(1−z5)b5⋯(1−z32)b32,where the bk 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, b32.