Integral Points on a Class of Elliptic Curve

摘要

We prove all integral points oi the elliptic curve y~2 = x~3 - 30x + 133 are (x, y) = (-7,0), (-3, ±14), (2, ±9),(6, ±13), (5 143 326, ±11 664 498 677), by using the method of algebraic number theory and p-adic analysis, Furthermore, we develop acomputation method to find all integral points on a class of elliptic curve y~2 = (x + a) (x~2 — ax + 6), a,b Z, a~2 < 4b and find all integer solutions of hyperelliptlc Diophantine equation Dy~2 = Ax~4 + Bx2 + C,B~2 < 4AC.