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perfect number = sum of two perfect cubes

Source: Ukraine TST 2012 p3

April 29, 2020
perfect cubesum of cubesnumber theoryperfect number

Problem Statement

A natural number nn is called perfect if it is equal to the sum of all its natural divisors other than nn. For example, the number 66 is perfect because 6=1+2+36 = 1 + 2 + 3. Find all even perfect numbers that can be given as the sum of two cubes positive integers.
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