纯粹数学与应用数学
純粹數學與應用數學
순수수학여응용수학
PURE AND APPLIED MATHEMATICS
2013年
4期
342-349
,共8页
Je′smanowicz猜想%丢番图方程%同余
Je′smanowicz猜想%丟番圖方程%同餘
Je′smanowicz시상%주번도방정%동여
Je′smanowicz′ conjecture%Diophantine equation%congruence
运用同余及元素阶的性质,证明了对任意的正整数n,丢番图方程(195n)x+(28n)y=(197n)z仅有正整数解(x, y, z)=(2,2,2)。
運用同餘及元素階的性質,證明瞭對任意的正整數n,丟番圖方程(195n)x+(28n)y=(197n)z僅有正整數解(x, y, z)=(2,2,2)。
운용동여급원소계적성질,증명료대임의적정정수n,주번도방정(195n)x+(28n)y=(197n)z부유정정수해(x, y, z)=(2,2,2)。
In this paper, using the properties of congruences and the order of elements, we show that for any positive integer n, the Diophantine equation (195n)x+(28n)y =(197n)z has no solution other than (x, y, z)=(2, 2, 2) in positive integers.
