Fermat's Last Theorem: Latin: Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos & generaliter nullam in infinitum ultra quadratum pote

Fermat's Last Theorem: Latin: Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos & generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet. Translation: It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a truly marvelous proof of this, which this margin is too narrow to contain. https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem Fermat's Little Theorem (much more useful in practice): French:Tout nombre premier mesure infailliblement une des puissances − 1 de quelque progression que ce soit, et l'exposant de la dite puissance est sous-multiple du nombre premier donné − 1; et, après qu'on a trouvé la première puissance qui satisfait à la question, toutes celles dont les exposants sont multiples de l'exposant de la première satisfont tout de même à la question. Translation: Every prime number [p] divides necessarily one of the powers minus one of any [geometric] progression [x, x², x³, ... ] [that is, there exists a such that p divides xª – 1], and the exponent of this power [a] divides the given prime minus one [divides p – 1]. After one has found the first power [a] that satisfies the question, all those whose exponents are multiples of the exponent of the first one satisfy similarly the question [that is, all multiples of the first a have the same property]. https://en.wikipedia.org/wiki/Fermat%27s_little_theorem https://en.wikipedia.org/wiki/Fermat%27s_little_theorem