### Instruction: What is the greatest product obtainable from two integers whose sum is 1998?### Response: I want to maximize the product of two numbers that add up to 1998, so I should think about how the product of two numbers changes as they get closer or farther apart.
If I fix one number at a certain value, say x, then the other number is 1998 - x, and their product is x(1998 - x).
I can think of this as a quadratic function of x, and I know that quadratic functions have a maximum value when x is equal to the average of the roots.
The roots of this function are when x = 0 and when x = 1998, so the average of those is 999.
That means the product is maximized when both numbers are 999, and their product is 999^2.
I could also use calculus and take the derivative of the function, but that would give me the same result.