Diophantine equation,an indispensable branch of number theory,has a long history and rich content,and its theory and method are widely used in various disciplines and practical life.In this paper,the integer solutions of indefinite equation x2-1 = 114y2 are discussed by means of congruence,recursive sequence,quadratic residue and properties of the solution of the Pell equation.Firstly,the original indefinite equation is decomposed into 8 cases by factorization.Secondly,the eight cases are analyzed by transformation and mod ulo taking techniques.Finally,the only integer solution(x,y)=(1,0)is obtained for the indefinite equation x2-1 =114y2.
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