关于Abel差集的一个猜想

A conjecture on Abelian difference sets

设p是奇素数。运用初等数论方法证明了:方程x2=22a+2p2n-2a+2pn+r+1没有适合n≥r的正整数解(x,a,n,r)。上述结果部分地分解决了S.L.Ma有关Abel差集的一个猜想。

Let p be an odd prime.By using some elementary number theory methods,it is shown that the equation x^2=2^2a＋2p^2n-2a＋2^pn＋r＋1 has no positive integer solution（x,a,n,r） with n≥r.This result partly solves a S.L.Ma＇s conjecture on Abelian difference sets.