Unfortunately this is most likely not correct It is believed that Fermat had an idea but didn't know it couldn't work. He hinted at those methods in other work

Unfortunately this is most likely not correct It is believed that Fermat had an idea but didn't know it couldn't work. He hinted at those methods in other works of his, but in the end that couldn't work. (Of course he might have found a different way, but it's a very low chance)