Question

Given a positive integer N, find all of the positive integers from 1 to N that can be written as a sum of 2 cubic numbers (also have to be positive) in two different ways.

Answer 1

There are infinite such positive integers which can be written as a sum of cubes of two positive integers. Some of them are written below:

• 1³+12³=9³+10³=1729
• 2³+24³=18³+20³=13832
• 10³+27³=19³+24³=20683
• 15³+945³=744³+756³=843912000

Hence it is not possible to write all such numbers which can be written in this format. Though some of them can be enlisted if the value of maximum integer "N" is given.