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It's a problem in which a, b, and c are constants, x, y, and z are to be found, and

some company in England will award $1 million to the first person who solves it.

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As stated it is a simple power equation - nothing special about it. It gets interesting only if the variables are all integers.

When x = y = z = 1 the solution set is, trivially, the solutions to a + b = c.

When x = y = z = 2, then the solution set consists of Pythagorean triples.

When x = y = z > 2, then the equation becomes Fermat's Last Theorem which has now been proven to have NO solutions.

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11y ago

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