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On the surface, it seems easy. Can you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. One answer is x = 1, y = -1, and z = 2. But what about the integers for x, y, and z so that x³+y³+z³=42?
That turned out to be much harder—as in, no one was able to solve for those integers for 65 years until a supercomputer finally came up with the solution to 42. (For the record:
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In 2019, mathematicians finally solved a math puzzle that had stumped them for decades. It's called a Diophantine Equation, and it's sometimes known as the “summing of three cubes”: Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100. On the surface, it seems easy.
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