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He noted without proof, although he claimed to have discovered one, the assertion now known as Fermat's Last Theorem, which states that the equation xn _+_ yn _=_ zn , where x, y, z, and n are nonzero integers, has no solutions for n that are greater than 2. Prizes were offered for a proof of this theorem, and attempted proofs resulted in many developments in the theory of numbers. British mathematician Andrew Wiles described a proof of the conjecture in 1993, but a gap in the proof required additional work, which was completed in 1994. However, Wiles's proof involved mathematical concepts that were unknown in Fermat's lifetime, so whether Fermat had a valid proof remains conjecture.
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