指数Diophatine方程p^a-p^b+p^c=z^2

The exponential diophantine eouation p^a-p^b+p^c=z^2

设p是奇素数.本文运用有关广义Ramanujan-Nage11方程的深刻结果,给出了方程pa-pb+pc=z2的全部非负整数解(a,b,c,z).

Let p be an odd prime. Using a deep result related to the generalized Ramanujan - Nagell equation, all nonnegative integer solution （a ,b ,c ,z） of the equation P^a-P^b＋P^c=z^2 are given.