n. the celebrated conjecture in number theory that the equation xⁿ + yⁿ = zⁿ, does not have non-trivial integral solutions for x, y, z when n is greater than 2 (when n = 2 Pythagoras' theorem shows the existence of solutions). Fermat annotated his copy of a translation of Diophantus with `I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.' This claim is not now given much credence. In 1994, Andrew Wiles announced a proof of Fermat's last theorem using algebraic geometry which is now widely accepted. See also Waring's problem.