SOLUTION: What is the largest number which is the product of positive integers whose sum is 2005?

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Question 648576: What is the largest number which is the product of positive integers whose sum is 2005?
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Let x and y be positive integers.
Then let x*y be maximized by x+y = 2005
In general, the closer you get to a square, the larger the product will be. We can either use this fact, or we can make a table. I'll leave you to make a table if you want. Knowing that 2005 is odd, x and y can differ by at most one.
x + x+1 = 2005
2x = 2004
x = 1002
(1002+1) is the other.
Then 1002 and 1003 are the two integers.
Their product is 1005006.