Recent results about Fermat's last theorem (Q1083469)

This very readable survey describes firstly the work of \textit{M. Filaseta} [C. R. Math. Acad. Sci., Soc. R. Can. 6, 31-32 (1984; Zbl 0533.10010)], \textit{A. Granville} [ibid. 7, 55-60 (1985; Zbl 0565.10016)] and the reviewer [Bull. Lond. Math. Soc. 17, 15-16 (1985; Zbl 0546.10012)] on applications of Falting's theorem to Fermat's last theorem, and secondly the work of \textit{E. Fouvry} [Invent. Math. 79, 383-407 (1985; Zbl 0557.10035)], \textit{L. M. Adleman} and the reviewer [ibid. 79, 409-416 (1985; Zbl 0557.10034)] on the first case of Fermat's last theorem. Proofs of the easier results are given in full, and sketches of the more difficult ones. A number of new results on the problem are mentioned.