Abstract: In this paper, it is proved that the only intcger solutions of the equationx3+1=14y2 are(x,y)=(-1,0) and(5,±3),and tbe only intcger seluticon of equation x3-1=14y2 is(x,y)=(1,0).

Key words: indeterminate equation, intcgcr sloution, Jacobi symbol, reeurrent sequence

摘要： 本文证明了不定方程x3+1=14y2仅有整数解(x,y)=(-1,0)、(5,±3);ｘ3-1=14y２仅有整数解(x,y)=(1,0).

关键词: 不定方程, 整数解, Jacobi符号, 递归序列