We prove all integral points of the elliptic curve y^2=x^2-30x＋133 are （x,y） = （-7,0）,（-3,±14）,（2, ±9）,（6,±13）, （5143326,±11664498677）, by using the method of algebraic number theory a...We prove all integral points of the elliptic curve y^2=x^2-30x＋133 are （x,y） = （-7,0）,（-3,±14）,（2, ±9）,（6,±13）, （5143326,±11664498677）, by using the method of algebraic number theory and p-adic analysis. Furthermore, we develop a computation method to find all integral points on a class of elliptic curve y^2= （x＋α）（x^2-α）（x^2-αx＋b） ,α ,b∈Z,α^2〈4b and find all integer solutions of hyperelliptic Diophantine equation Dy^2=Ax^4 ＋ Bx^2 ＋C,B^2〈4AC.展开更多
基金Supported by the National Natural Science Foun-dation of China (2001AA141010)
文摘We prove all integral points of the elliptic curve y^2=x^2-30x＋133 are （x,y） = （-7,0）,（-3,±14）,（2, ±9）,（6,±13）, （5143326,±11664498677）, by using the method of algebraic number theory and p-adic analysis. Furthermore, we develop a computation method to find all integral points on a class of elliptic curve y^2= （x＋α）（x^2-α）（x^2-αx＋b） ,α ,b∈Z,α^2〈4b and find all integer solutions of hyperelliptic Diophantine equation Dy^2=Ax^4 ＋ Bx^2 ＋C,B^2〈4AC.
