The number of the ordered pairs of intergers (m,n) for which mn> or = 0
and m cubed + n cubed +99mn = 33 cubed is equal to ?
a. 2 b. 3 c. 33 d. 35 e. 99
Initially my answer was a. 2 ( 0, 33 ) (33, 0 ) but I know there would be more pairs. How do I find the other pairs without randomly plugging in numbers?
orThe first of these possibilities, , gives integer solutions for ; namely .
I'm not yet sure how to proceed with the second one. is a solution:but I'm not sure how to show that this is the only one.
Anyway, there are your 35 solutions: and .