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May 22nd, 2016, 03:49 PM   #1
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Compare two sums of products without direct computation?

Say you have two sums of products and you want to know which sum is greater. All factors are positive integers. The factors in each product are generally small (< 10), but there may be many of them (in the thousands). Is there a way of determining which sum is greater without directly computing the products?
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May 22nd, 2016, 11:32 PM   #2
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Is there any limit to the factors in each product or how many products are in the sum?
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May 23rd, 2016, 07:50 PM   #3
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Either quantity could be in the millions. The quantity of factors per product will be equal, although the quantity of terms in sums will generally be unequal. As far as magnitude, each factor will be between 1 and 9, inclusive.
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