If m and n are positive integers and m^2 + n^2 = 137, what is the value of m^3 + n^3?
Choose the correct choice from the following options
A) 72
B) 224
C) 320
D) 512
E) 1,395
You need to integers which squared are equal 40.   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   9^2 = 81   10^2 = 100   11^2 = 121   Stop. The integers can't be greater than 6 or we will score above 137.   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   9^2 = 81   10^2 = 100   11^2 = 121   The only pair that matches is 11^2 + 4^2 = 137.   So 11^3 + 4^3 = 1395.   Answer 1,395.)
<result>E</result>
If m and n are positive integers and m^2 + n^2 = 137, what is the value of m^3 + n^3?