Hatcher-Topology-of-Numbers · Problem 13

The Farey Diagram

Mathematics — Algebraic Topology · sums-of-squares-congruences

Problem

Use congruences modulo 8 to show that primitive solutions of

a^2 + b^2 + c^2 = d^2

must have

d

odd and must have two of

a, b, c

even and the other odd.