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논문 기본 정보
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- 학술저널
- 저자정보
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- 한국전산응용수학회 Journal of applied mathematics & informatics Journal of applied mathematics & informatics 제27권 제1호
- 발행연도
- 2009.1
- 수록면
- 89 - 96 (8page)
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In this article, we show a generalization of Clement's theorem on the pair of primes. For any integers n and k, integers n and n + 2k are a pair of primes if and only if 2k(2k)![(n - 1)! + 1] + ((2k)! - 1)n ${\equiv}$ 0 (mod n(n + 2k)) whenever (n, (2k)!) = (n + 2k, (2k)!) = 1. Especially, n or n + 2k is a composite number, a pair (n, n + 2k), for which 2k(2k)![(n - 1)! + 1] + ((2k)! - 1)n ${\equiv}$ 0 (mod n(n + 2k)) is called a pair of pseudoprimes for any positive integer k. We have pairs of pseudorimes (n, n + 2k) with $n{\leq}5{\times}10^4$ for each positive integer $k(4{\leq}k{\leq}10)$.
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참고문헌 (7)
참고문헌 신청
G.H. Hardy / 1966 / Some problems of ”Partitio Numerrorum”, III: On the expression of a number as a sum of primes / Clarendon Press :561~630
Y.Y. Park / 2003 / On the sevral differences between primes / J. Appl. Math. & Computing 13:37~51
H.S. Lee / 2006 / On the primes with pn+1−pn = 8 and the sum of their reciprocals / J. Appl. Math. & Computing 22:441~452
D.M. Burton / 1980 / Elementary number theory / McGraw-Hill :97~98
P. Ribenboim / 1996 / The new book of prime number records / Springer :25~26
Y.Y. Park / 2003 / On the sevral differences between primes / J. Appl. Math. & Computing 13:37~51
H.S. Lee / 2006 / On the primes with pn+1−pn = 8 and the sum of their reciprocals / J. Appl. Math. & Computing 22:441~452
D.M. Burton / 1980 / Elementary number theory / McGraw-Hill :97~98
P. Ribenboim / 1996 / The new book of prime number records / Springer :25~26
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