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Check out the big brain on Beal!
Andrew Beal came up with this twenty years ago:
If Ax + By = Cz, where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common prime factor.
First, that will make sense to Mrs. LL and the Freshman In The House, but I'm not a 100% clear on what's going on there. But that's not the point of this post. This is: The $1 million goes to anyone who can "prove or disprove his conjecture."
I understand the disproving part: Get lucky enough to plug in a series of numbers (positive integers and greater than 2, as required) that don't have A, B, and C with a "common prime factor." Ta-da! Theory disproved.
But how would you prove that it is always true? Set up some computer program that just keeps printing out result after result which shows it's true? But just because the formula is true for the first billion equations a computer runs doesn't necessarily mean it will be true on the next one.
Source.
