丢番图方程y(y+1)(y+2)=2x(x+1)(x+2)的整数解

The Integer Solution on the Diophantine Equation y (y+1) (y+2)=2x (x+1) (x+2)

关键词:  丢番图方程  整数解  有效常数

Key words:  Diophantine equation  integer solutiion  effective constant

摘要:

证明丢番图方程y(y+1)(y+2)=dx(x+1)(x+2)的所有整数解满足max{︱x︱,︱y︱}<C,其中,d是一个给定整数,C为仅依赖于d的有效常数.特别地,给出当d=2时方程的全部整数解.

Abstract:

Let d be a given integer, all integer solutions of the diophantine equationcan y (y+1) (y+2)=dx (x+1) (x+2)are effective determined, i.e.max {|x|, |y|}<C (effectively computable constant depending only d).In particular, all solutions can be determined when d=2.