## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Thursday, November 18, 2021 — 4:00 PM EST

**Nicolas Banks, Department of Pure Mathematics, University of Waterloo**

"ABC Conjecture and Fermat's Last Theorem for Polynomials"

The ABC conjecture, posed in the 1980s, asserts (roughly) that if integers A and B are divisible by large powers of small primes, then their sum C=A+B is usually divisible by small powers of large primes. It has a number of important consequences, both known and unknown, such as Roth's theorem on approximations of rational numbers, Faltings' theorem on rational points on projective curves, and the Fermat-Catalan conjecture, which generalizes Fermat's Last Theorem. Despite a claimed proof by Mochizuki in the last decade, the conjecture is still considered unproved by the general mathematical community.

There is an analogous result for polynomials called the Mason-Stothers theorem. Oddly, this theorem is far easier to prove. In fact, an elegant elementary proof was discovered by a high school student in 2000. We present this proof, then use it to prove an analogue of Fermat's Last Theorem for polynomials.

Zoom meeting: https://uwaterloo.zoom.us/j/95669082908?pwd=L0NhbVZBakFGQXUycUZka01CL2lsQT09

Event tags

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.