A note written in 1637 in the margin of a book says that there are no positive integers x, y and z such that xn + yn = zn, where n is an integer greater than two. This wasn't proved until 1995. Who is the author of this note?
Fermat's Last Theorem the "Guinness Book of World Records" as the "most difficult mathematical problem", one of the reasons being that it has the largest number of unsuccessful proofs. The Pythagorean equation, , has an infinite number of positive integer solutions for "x", "y", and "z"; these solutions are known as Pythagorean triples. Around 1637, Fermat wrote in the margin of a book that the more general equation had no solutions in positive integers, if "n" is an integer greater than 2. Although he claimed to have a general proof of his conjecture, Fermat left no details of his proof, and no proof
Proof that π is irrational be 0, because otherwise it would follow from claim 1 that each "f"("x") ("n" ∈ N) would be 0, which would contradict claim 2. Now, take a natural number "c" such that all three numbers "bc"/"k", "ck"/"x" and "c"/"x" are integers and consider the sequence Then On the other hand, it follows from claim 1 that which is a linear combination of "g" and "g" with integer coefficients. Therefore, each "g" is an integer multiple of "y". Besides, it follows from claim 2 that each "g" is greater than 0 (and therefore that "g" ≥ |"y"|) if "n" is large