If m and n are positive integers and m^2 + n^2 = 89, what is the value of m^3 + n^3?
Choices:  A) 72  B) 224  C) 320  D) 512  E) 637
You need to integers which squared are equal 89.   Which could it be ? Let's start with the first integer:   1^2 = 1   2^2 = 4   3^2 = 9   4^2 = 16   5^2 = 25   6^2 = 36   7^2 = 49   8^2 = 64   Stop. The integers can't be greater than 8 or we will score above 89.   The second integer need to be picked up the same way.   1^2 = 1   2^2 = 4   3^2 = 9   4^2 = 16   5^2 = 25   6^2 = 36   7^2 = 49   8^2 = 64   The only pair that matches is 8^2 + 5^2 = 89.   So 8^3 + 5^3 = 637.   Answer 637.)
<result>E</result>
If m and n are positive integers and m^2 + n^2 = 89, what is the value of m^3 + n^3?