MACM 101 Lecture Notes - Lecture 15: The Last Theorem, Andrew Wiles
13 Aug 2016
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For n > 2, the equation xn + yn = zn. Has no nontrivial integer solutions (fermat"s last theorem was proven by andrew wiles in 1994) If given a question to prove or disprove a predicate is universally true, say e. g. x is a positive integer p(x): x is prime. We should observe that disproving will be a lot easier than proving. Because all we have to do is a single example of an x for which p(x) is false. It is common (but erroneous) approach to prove by giving an example that works. Well, 2 is a prime and 3 is a prime. Proof by example is no more convincing when used on a true statement. Proof: since 2|6 and 6|30, we have a|b and b|c. What we need is a proof where we don"t care about the values of x, a, b, c.
