Question

The number 1729 is the smallest number that can be expressed as the sum of two cubes in two different ways as 1729 = 12^3 + 1^3 = 10^3 + 9^3. Find two other numbers with the same property. Express them as the sum of two cubes.

Answer 1

Answer:

4104 and 13832

Step-by-step explanation:

This type of number is known as the Hardy-Ramanujan Number.

We have that 1729 is the first number where this is found, but there are others. The second number that meets this is:

4104

2 ^ 3 + 16 ^ 3 = 9 ^ 3 + 15 ^ 3

And we also have:

13832

18 ^ 3 + 20 ^ 3 = 2 ^ 3 + 24 ^ 3

That is to say, the numbers 4104 and 13832 comply with this property