Hatcher-Topology-of-Numbers · Problem 14

The Farey Diagram

Mathematics — Algebraic Topology · fermats-last-theorem-rational-points

Problem

Show that if the curve

x^n + y^n = 1

has a rational point with

x

and

y

nonzero, then it has a rational point with

x

and

y

positive. Hint: Consider the equation

a^n + b^n = c^n