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USAMO
1988


Problem - 3529
A polynomial product of the form (1z)b1(1z2)b2(1z3)b3(1z4)b4(1z5)b5(1z32)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 12z. Determine, with proof, b32.

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