On a resultant connected with Fermat's last theorem

Certain Congruence Criteria Connected with Fermat's Last Theorem.

A fourteenth lecture on Fermat’s Last Theorem∗

The title of this lecture alludes to Ribenboim’s delightful treatise on Fermat’s Last Theorem [Rib1]. Fifteen years after the publication of [Rib1], Andrew Wiles finally succeeded in solving Fermat’s 350-year-old conundrum. That same year, perhaps to console himself of Fermat’s demise, Ribenboim published a second book, this time on Catalan’s conjecture that there are no consecutive perfect pow...

ON POINCARFv'S LAST GEOMETRICAL THEOREM

1. Let R be an annulus with inner radius a and outer radius b; i.e. the set of all points (x, y) such that a2^r2 = x2+y2^2>2. Let T be a homeomorphism of R onto itself, keeping the bounding circles fixed. If we introduce polar coordinates (r, 8), (O=0<27r) we may write T(r, 8) = (r't 0') where 6' is determined mod 2ir. For a particular point (r0, do) choose some determination 80* of do and cons...

Fermat’s Last Theorem

Fermat learned his number theory from the books of Diophantus; it was in the margins of his copy that he wrote down that he had discovered a truly marvelous proof of the fact that X + Y n = Z has no solutions in natural numbers for n > 2, and that the margin was too small to contain it. The books of Diophantus, including these remarks, were published posthumously by his son. By the early 1800s,...

Fermat's Last Theorem

The authors would like to give special thanks to N. Boston, K. Buzzard, and B. Conrad for providing so much valuable feedback on earlier versions of this paper. They are also grateful to A. Agboola, M. Bertolini, B. Edixhoven, J. Fearnley, R. Gross, L. Guo, F. Jarvis, H. Kisilevsky, E. Liverance, J. Manoharmayum, K. Ribet, D. Rohrlich, M. Rosen, R. Schoof, J.-P. Serre, C. Skinner, D. Thakur, J....