Mersenne数$M_p$都是孤立数

All Mersenne Numbers Are Anti-Sociable Numbers

中文关键词:  Mersenne数  相亲数  孤立数.

英文关键词:Mersenne number  amicable pair  anti-sociable number.

中文摘要:

      设$p$是素数, $M_{p}=2^{p}-1$.本文证明了$M_{p}$都是孤立数.

英文摘要:

      Let $p$ be a prime, and let $M_{p}=2^{p}-1$. This paper proves that $M_{p}$ is an anti-sociable number.