关于不定方程y(y+1)(y+2)(y+3)=4n^2x(x+1)(x+2)(x+3)

On the Diophantine Equation y(y+1)(y+2)(y+3)=4n^2x(x+1)(x+2)(x+3)

设1<n∈N^*,运用Pell方程的一些结果以及代数数论和p-adic分析方法证明了不定方程y(y+1)(y+2)(y+3)=4n^2x(x+1)(+2)(x+3)(x,y∈N^*)除开n=1189时仅有一组解(x,y)=(33,1680)外,无其他解.

Let 1<n E N^*,In this paper,using the results on some Pell equations and algebraic number theory and p-adic analysis method,we prove that the Diophantine equation y(y+1)(y+2)(y+3)=4 n^2 x(x+1)(x+2)(x+3)(x,y∈N^*)has no solution except n=1189 in which the equation has one solution(x,y)=(33,1680).