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Fermat's last theorem was a mathematical result written down by Fermat in 1637; but after his death in 1665 no-one could find any evidence that he had actually proved his theorem. When was the result finally proved?

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Fermat's last theorem was a mathematical result written down by Fermat in 1637; but after his death in 1665 no-one could find any evidence that he had actually proved his theorem. When was the result finally proved?