Are they both perfect cubes?
Find the sum of all ordered pairs of positive integers such that both and are perfect cubes.
If none such pair exists then enter 0.
The answer is 0.
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1 solution
Assume the contrary.Let, 3 m + n = a 3 and 3 m 2 + n 2 = b 3 . Multiplying them and some algebra gives, ( 2 m ) 3 + ( m + n ) 3 = ( a b ) 3 which contradicts the fermat's last theorem. Hence,no such pair exist and the answer is 0.