Journal of Shanghai University(Natural Science Edition)
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ZHOU Bin-bin
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Abstract: Perfect number, amicable number and anti-sociable numbers are important topics in number theory. Recently, advances have been made in anti-sociable numbers. In 2000, F.LUCA proved that Fermat number are anti-sociable numbers, and in 2005, M.H. LE proved all powers of 2 are anti-sociable numbers. We have used the method of M.H. LE to obtain some new results of the antisociable numbers. For every integer n containing prime divisors that are 1 mod 4, let pmod 4 be an arbitrary prime divisor of n. There is at least one anti-sociable number inn2, p2n2, p4n2, and p6n2. Therefore we can prove that anti-sociable numbers have positive density in perfect square numbers. We also give a method to find the exact anti-sociable numbers.
Key words: amicable number, congruence, anti-sociable number
CLC Number:
O 156.1
ZHOU Bin-bin. New Results of Anti-Sociable Numbers[J]. Journal of Shanghai University(Natural Science Edition).
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URL: https://www.journal.shu.edu.cn/EN/
https://www.journal.shu.edu.cn/EN/Y2008/V14/I4/394