科研之友
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摘要
Let a be a positive integer, and let p(1), p(2) be two distinct prime numbers with p(1) < p(2). By using elementary methods, we give two equivalent conditions of all even near-perfect numbers in the form 2 alpha p(1)p(2) and 2(alpha)p(1)(2)p(2), and obtain a lot of new near-perfect numbers which involve some special kinds of prime number pairs. One kind is exactly the new Mersenne conjecture's prime number pair. Another kind has the form p(1) = 2(alpha+1) - 1 and p(2) = p(2)(1)+p(1)+1/3, where the former is a Mersenne prime and the latter's behavior is very much like a Fermat number.
- 出版日期2015-7
- 单位四川师范大学
