Generalized Identities on the Products of Fibonacci-Like and Lucas Numbers

Shikha Bhatnagar, Omprakash Sikhwal

Abstract


The Fibonacci, Fibonacci-Like and Lucas sequences are shining stars in the vast array of integer sequences. They have fascinated both amateurs and professional mathematicians for centuries. Also they continue to charm us with their beauty, their abundant applications and their ubiquitous habit of occurring in totally surprising and unrelated places. The product of Fibonacci number and Lucas number is a linear function of Fibonacci numbers. In this paper, we investigated some generalized identities on products of Fibonacci-Like and Lucas numbers. Further we showed that product is commutative when same location numbers will be taken in reverse order.


Full Text:

PDF

References


B. Singh, P. Bhadouria, O. Sikhwal, “Generalized identities involving common factors of Fibonacci and Lucas numbers”, International Journal of Algebra, Vol. 5, No. 13, pp. 637-645, 2011.

B. Singh, O. Sikhwal, S. Bhatnagar, “Some identities for even and odd Fibonacci-Like and Lucas numbers”, Proc. National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing, USA, 2011, pp 4-6.

B. Singh, O. Sikhwal, S. Bhatnagar, “Fibonacci-Like sequence and its properties”, , International Journal of Contemporary Mathematical Sciences, Vol. 5, No. 18, pp. 859-868, 2010.

M. Thongmoon, “Identities for the common factors of Fibonacci and Lucas numbers”, International Mathematical Forum, Vol. 4, no. 7, pp. 303-308, 2009.

M. Thongmoon, “New identities for even and odd Fibonacci and Lucas numbers”, International Journal of Contemporary Mathematical Sciences, Vol. 4, No. 14, pp. 71–676, 2009.

T. Koshy, “Fibonacci and Lucas numbers with applications”, New York, NY, USA, Wiley-Interscience, 2001.

T. Koshy, “Sums of Fibonacci–Pell–Jacobsthal products”, International Journal of Mathematical Education in Science and Technology, Vol. 44, No. 4, pp. 559-568, 2013.

Z. Cerin, “Sums of products of generalized Fibonacci and Lucas numbers”, Demonstratio Mathematica, Vol. 42, No. 2, pp. 211-218, 2009.


Refbacks

  • There are currently no refbacks.


MAYFEB Journal of Mathematics 
Toronto, Ontario, Canada
MAYFEB TECHNOLOGY DEVELOPMENT
ISSN 2371-6193