2018 teaser
Find the value of such that the sum of positive numbers is 2018 and the product of these same numbers is maximized.
Bonus:
Generalize this for the sum of
.
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1 solution
For any integer N... By AM GM Inequality we know that all the partitions should be equal. So we need to find the minimum value of (N/x)^x where x is the number of partitions. By differentiating the function and putting it equal to 0. We get x=(N/e), where e is euler's number. Here N is 2018 so we get x=742.38 . So the nearest option is 742.