본문 바로가기
KERD
논문KCI 등재

THE STRUCTURAL RELATIONSHIPS BETWEEN FIBONACCI AND PRIME-GENERATED ODD-NUMBER SEQUENCES

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

The prime-generated odd-number sequence Np = 2p-1, p prime, can yield some prime values for Np and these are used as indicators of Fibonacci Fp composites. This structural characteristic of integers yields a type of primality test which in turn enables composite Fp with factors of the form pk + 1 to be identified up to p = 727

Abstract

The prime-generated odd-number sequence Np = 2p-1, p prime, can yield some prime values for Np and these are used as indicators of Fibonacci Fp composites. This structural characteristic of integers yields a type of primality test which in turn enables composite Fp with factors of the form pk + 1 to be identified up to p = 727

참고문헌 (15)

  1. Carmichael, R. D., "On the Numerical Factors of the Arithmetic Forms αn±βn", Annals of Mathematics, 15(1), pp.30~70 (1913)
  2. Drobot, V., "On Primes in the Fibonacci Sequence", The Fibonacci Quarterly, 38(1), pp.71~72 (2000)
  3. Franklin, James, "An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure", pp.217~218 (2014), Palgrave Macmillan
  4. Leyendekkers, J. V., "Fibonacci and Lucas Primes", Notes on Number Theory & Discrete Mathematics, 19(2), pp.49~59 (2013)
  5. Leyendekkers, J.V., "The Pascal-Fibonacci Numbers", Notes on Number Theory & Discrete Mathematics, 19(3), pp.49~59 (2013)
  6. Leyendekkers, J. V., "Fibonacci Primes", Notes on Number Theory & Discrete Mathematics (2014)
  7. Leyendekkers, J. V., "Fibonacci Numbers with Prime Subscripts: Digital Sums for Primes versus Composites", Notes on Number Theory & Discrete Mathematics (2014)
  8. Leyendekkers, J.V., "Fibonacci Number Sums as Prime Indicators", Notes on Number Theory & Discrete Mathematics (2014)
  9. Leyendekkers, J. V., "Pell and Lucas Primes", ~ (2014)
  10. Shannon, A. G., "Carlitz Generalizations of Lucas and Lehmer Sequences", The Fibonacci Quarterly, 31(2), pp.105~111 (1993)
  11. Shannon, A. G., "Bioprocess Engineering and the Manners-Gandolfi X-ray Camera", International Journal Bioautomation, 14(3), pp.171~178 (2010)
  12. Somer, L., "Generalization of a Theorem of Drobot", The Fibonacci Quarterly, 40(4), pp.435~437 (2002)
  13. Stewart, C. L., "Transcendence Theory: Advances and Applications", pp.79~92 (1977), Academic Press
  14. Terr, David, "On the Sums of Digits of Fibonacci Numbers", The Fibonacci Quarterly, 34(4), pp.349~355 (1996)
  15. Yabuta, Minoku, "A Simple Proof of Carmichael's Theorem on Primitive Divisors", The Fibonacci Quarterly, 39(5), pp.439~443 (2001)

관련 논문AI추천

이 간행물의 다른 논문 (11건)