I was reading a pdf (Arithmetic Progressions of Three Squares by Keith Conrad) and I have a question about Theorem 3.5. It says that we can use Dirichlet's theorem on primes in arithmetic progression to prove the Theorem, but the proof is on pages 44-45 and I can't find it. Does anyone know the proof with Dirichlet's theorem or have the pages 44-45 from Arithmetic Progressions of Three Squares ?
"Theorem 3.5. For rational $ n\neq 0 $, the only nonidentity rational points on $ y^2=x^3-n^2x $ of finite order are $ (0,0), (n,0), and (-n,0) $. "