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Let α be a positive integer, and let p1, p2 be two distinct prime numbers with p1 < p2. By using elementary methods, we give two equivalent conditions of all even near-perfect numbers in the form 2αp21p2 and 2αp21p2, 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 p1=2α+1-1 and p2=p21+p1+1/3, where the former is a Mersenne prime and the latter’s behavior is very much like a Fermat number.
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참고문헌 (13)
참고문헌 신청
B. Stubblefield / 1977 / Greater lower bounds for odd perfect numbers / Env. Res. Lab. NOAA : 209 ~
G. H. Hardy / 2003 / An Introduction to the Theory of Numbers / Oxford Science Publishers
K. Ireland / 1990 / A Classical Introduction to Modern Number Theory / Springer
M. M. Buxton / 1976 / An extension of lower bounds for odd perfect numbers / Not. Amer. Math. Soc 23 : A-55 ~
M. Tang / 2013 / On near-perfect and deficient-perfect numbers / Colloq. Math 133 (2) : 221 ~ 226
G. H. Hardy / 2003 / An Introduction to the Theory of Numbers / Oxford Science Publishers
K. Ireland / 1990 / A Classical Introduction to Modern Number Theory / Springer
M. M. Buxton / 1976 / An extension of lower bounds for odd perfect numbers / Not. Amer. Math. Soc 23 : A-55 ~
M. Tang / 2013 / On near-perfect and deficient-perfect numbers / Colloq. Math 133 (2) : 221 ~ 226
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