Integer solution of Diophantine equation x3+1=603y2
Let D contain prime factors of type 6k+1,where k is a positive integer,the solution of the Diophantine equation x3+1=Dy2(D＞0)has always been one of the unsolved topics in number theory.By using some elementary methods,such as congruence,recursive sequence,quartic Diophantine equation,factorization and the properties of the solutions to Pell equation,and combining with elementary number theory method and the mathematical idea of classification discussion,the integer solution of the Diophan-tine equation x3+1=603y2 in different cases is studied.It is obtained that when D=603,the Diophantine equation has only one integer solution(x,y)=(-1,0).The conclusion can promote the research of this kind of equation.
NETL
NSTL
万方数据
