广义Mersenne数中的奇完全数

Odd Perfect Numbers in Generalized Mersenne Numbers

设p是奇素数,a和b是适合a>b,gcd(a,b)=1的正整数.设f(a,b,p)=(ap-bp)/(a-b).运用初等数论方法证明了当loga≤max(7logp,(2p-1-1)logp)时,f(a,b,p)不是奇完全数.

Let p be an odd prime,a and b be coprime positive integers with ab,gcd（a,b）=1.more over let f（a,b,p）=（ap-bp）/（a-b）.Using some elementary number theory methods,it is proved that if log a≤max（7log p,（2p-1-1）log p）,f（a,b,p） is not an odd perfect number.