Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Several proofs for Fermat's Last Theorem for specific exponents have been developed. Fermat's Last Theorem states that no three positive integers (a, b, c) can satisfy the equation an + bn = cn for any integer value of n greater than two. If n equals two, the equation has infinitely many solutions, the Pythagorean triples. A solution (a, b, c) for a given n is equivalent to a solution for all the factors of n. For illustration, let n be factored into g and h, n = gh. Then (ag, bg, cg) is a solution for the exponent h; (ag)h + (bg)h = (cg)h. Conversely, to prove that Fermat's equation has no solutions for n > 2, it suffices to prove that it has no solutions for n = 4 and for all odd primes p. For any such odd exponent p, every positive-integer solution of the equation ap + bp = cp corresponds to a general integer solution to the equation ap + bp + cp = 0.

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