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Jernej
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Paritioning a set of numbers A into two sets B,C so that abs(prod(B) - prod(C)) is minimal

Let A = {a_1,...,a_n} be a set of numbers. We can assume all elements of A are integers.

Is there any efficient way to partition A into two sets B = {b_1,...,b_k} and C = {c_1,...,c_l} such that abs((b_1*...*b_k) - (c_1*...*c_l)) is minimal?

Is the problem anything easier if we let A be a set of strictly positive integers? What if we only let prime numbers?

Jernej
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