Let m be a prime number not exceeding 31. Let p be prime, and let x, y, z be integers such that xp + yp + zp = 0. Assume that p does not divide the productxyz. Then, p² must divide mp − 1-1.
Review
Granville wrote that Morishima's proof could not be accepted. [1]
References
^Morishima, Taro (January 1952). "On Fermat's Last Theorem (Thirteenth Paper)". Transactions of the American Mathematical Society. 72 (1): 67–81. doi:10.2307/1990655. JSTOR1990655.
^Morishima, Taro; Y Karamatsu (1990). Collected papers of Taro Morishima. Kingston, Ontario, Canada: Queens University.