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A CLASS OF NEW NEAR-PERFECT NUMBERS
LI, YANBIN,LIAO, QUNYING Korean Mathematical Society 2015 대한수학회지 Vol.52 No.4
Let ${\alpha}$ 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 $2^{\alpha}p_1p_2$ and $2^{\alpha}p_1^2p_2$, 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 $p_2={\frac{p^2_1+p_1+1}{3}}$, where the former is a Mersenne prime and the latter's behavior is very much like a Fermat number.
ON GENERALIZED ZERO-DIFFERENCE BALANCED FUNCTIONS
Jiang, Lin,Liao, Qunying Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.1
In the present paper, by generalizing the definition of the zero-difference balanced (ZDB) function to be the G-ZDB function, several classes of G-ZDB functions are constructed based on properties of cyclotomic numbers. Furthermore, some special constant composition codes are obtained directly from G-ZDB functions.
A CLASS OF NEW NEAR-PERFECT NUMBERS
Yanbin Li,Qunying Liao 대한수학회 2015 대한수학회지 Vol.52 No.4
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.