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Partitioning a natural number $n$ in order to get the maximum product sequence of its addends
Given
$a_1+\cdots+a_n=k$
where $a_1$ to $a_n$ natural numbers what is the maximum number of
$a_1\times\cdots\times a_n$?
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william007
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For a start, look at the arithmetic-geometric mean inequality. Making the variables integers instead of real makes it more interesting. – marty cohen Jan 23 '13 at 03:28
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Prove that if two of the summands differ by more than $1$ then you can increase the product by making those two summands closer to each other. – Gerry Myerson Jan 23 '13 at 03:31