Topology of Numbers · Problem 10

The Farey Diagram — Allen Hatcher

Mathematics — Number Theory · congruences-diophantine-equations

Problem

(a) Show that the equation

x^2 - 2y^2 = \pm 3

has no integer solutions by considering this equation modulo 8. (b) Show that there are no primitive Pythagorean triples

(a, b, c)

with

a

and

b

differing by 3.