The Pythagorean Theorem - Educational Outreach

Fermat’s Last TheoremThe Diophantine equationn n nx y zwhere x , y , z , and n are all integers,has no nonzero solutions for n 2 .Fermat also claimed to have proof, but, alas, it wastoo large to fit in the margin of his copy of Arithmetica!Fermat’s Theorem and the tantalizing reference to a proofwere not to be discovered until after Fermat’s death in1665. Fermat’s son, Clement-Samuel, discovered hisfather’s work concerning Diophantine equations andpublished an edition of Arithmetica in 1670 annotated withhis father’s notes and observations.xn ynThe impossible integer relationship zn: n 2became known as Fermat’s LastTheorem—a theorem that could not be definitively proved ordisproved by counterexample for over 300 years until Wilesclosed this chapter of mathematical history in the two-yearspan 1993-1995. To be fair, according to current historians,Fermat probably had a proof for the case n 3 and the casen 4 . But a general proof for all n 2 was probablysomething way out of reach with even the bestmathematical knowledge available in Fermat’s day.***→132