1729 can be expressed as the sum of two perfect cubes in two distinct ways.
How many such numbers exist?
Hint: Given one set of such numbers, how could you construct another set?
If and are integers such that , then what is ?
In the above equations, there are respectively 2 and 3 positive integers whose sum is equal to their product.
Find 4 positive integers whose sum is equal to their product. Enter the answer as their sum
Find the positive integer such that is a perfect cube.
How many unordered 5-tuples of positive integers are there which satisfy the above equation?