# Almost a Pythagorean Triple

Number Theory Level pending

You're given a right triangle as shown above. If $$a$$ is a positive integer such that it satisfies the constraints $$a|c$$ and $$b^{2} = a! + (a-1)! + (a-2)!$$, what is the largest known value of $$a$$?

Hint: The related problem remains one of the world's unsolved math mysteries.

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