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Question: Some positive integers can be expressed as the sum of two cubes of positive integers. For example, 126 = 5^3 + 1^3. However, that's the only way of writing 126 as the sum of two cubes of positive integers. Find the smallest positive integer which is expressible as a sum of two cubes of positive integers in at least two different ways. Answer: One way to solve this problem is to try various combinations of numbers. Catherine found that 10^3 + 9^3 and 12^3 + 1^3 both equal 1729, which is in fact the answer. |
