Jon Perry wrote:

Excuse my ignorance please, but wrt to A. Wiles proof of FLT, is the proof valid for rationals and/or with rational powers?

If we keep the exponent n the same, and just allow the numbers a, b, c to be rational, there's certainly nothing new: just multiply a, b, and c by the same constant to clear their denominators. For rational exponents, there is a forthcoming paper "Fermat’s Last Theorem for Rational Exponents," by Curtis D. Bennett, A.M.W. Glass, and Gábor J. Szekely. Abstract copied from http://www.maa.org/pubs/monthly_apr04_toc.html --------- Fermat’s Last Theorem states that an + bn = cn has no positive integer solutions for n > 2. How does allowing for rational exponents with numerator greater than 2 and complex roots change the conclusion? Surprisingly, classical triangles and the laws of sines and cosines become embroiled in the proof that the only new solutions arise from taking sixth roots of unity and a, b, and c of equal modulus. --------- John McCarthy wrote:

How do you formulate the flt statement with rationals to exclude counterexamples like

1^(1/2) + 1^(1/2) = 4(1/2).

Remember, n>2! --Michael Kleber kleber@brandeis.edu