J. V. Leyendekkers and A. G. Shannon

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 19, 2013, Number 3, Pages 5—11

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## Details

### Authors and affiliations

J. V. Leyendekkers

*Faculty of Science, The University of Sydney
NSW 2006, Australia*

A. G. Shannon

*Faculty of Engineering & IT, University of Technology Sydney
NSW 2007, Australia*

### Abstract

The Pascal–Fibonacci (PF) numbers for a given Fibonacci number sum to give the values of that Fibonacci number. Individual PF numbers are members of one of the triangular, tetrahedral or pentagonal series or have factors in common with the pyramidal or other geometric series. For composite numbers, partial sums of PF numbers can yield a factor, while prime Fibonacci numbers are detected with sums of squares.

### Keywords

- Fibonacci numbers
- Binet equation
- Pascal Triangle
- Triangular numbers
- Tetrahedral numbers
- Pentagonal numbers
- Pyramidal numbers

### AMS Classification

- 11B39
- 11B50

### References

- Leyendekkers, J. V., A. G. Shannon. Fibonacci Numbers within Modular Rings.
*Notes on Number Theory and Discrete Mathematics*. Vol. 4, 1998, No. 4, 165–174. - Leyendekkers, J. V., A. G. Shannon. The Structure of Geometric Number Sequences.
*Notes on Number Theory and Discrete Mathematics*. Vol. 17, 2011, No. 3, 31–37. - Leyendekkers, J. V., A. G. Shannon. Geometric and Pellian Sequences.
*Advanced Studies in Contemporary Mathematics.*Vol. 22, 2012, No. 4, 507-508. - Leyendekkers, J. V., A. G. Shannon. The Structure of the Fibonacci Numbers in the Modular Ring
*Z*5.*Notes on Number Theory and Discrete Mathematics*. Vol. 19, 2013, No. 1, 66–72. - Leyendekkers, J. V., A. G. Shannon. On the Golden Ratio.
*Advanced Studies in Contemporary Mathematics*. Vol. 23, 2013, No. 1, 195–201. - Leyendekkers, J. V., A. G. Shannon. Fibonacci and Lucas Primes.
*Notes on Number Theory and Discrete Mathematics*. Vol. 19, 2013, No. 2, 49–59. - Shannon, A. G. Tribonacci Numbers and Pascal’s Pyramid.
*The Fibonacci Quarterly*. Vol. 15, 1977, No. 3, 268, 275. - Wong, C. K., T. W. Maddocks. A Generalized Pascal’s Triangle.
*The Fibonacci Quarterly*. Vol. 13, 1975, No. 2, 134–136.

## Related papers

## Cite this paper

APALeyendekkers, J. V., & Shannon, A. (2013). The Pascal–Fibonacci numbers. Notes on Number Theory and Discrete Mathematics, 19(3), 5-11.

ChicagoLeyendekkers, JV, and AG Shannon. “The Pascal–Fibonacci Numbers.” Notes on Number Theory and Discrete Mathematics 19, no. 3 (2013): 5-11.

MLALeyendekkers, Tieling, and AG Shannon. “The Pascal–Fibonacci Numbers.” Notes on Number Theory and Discrete Mathematics 19.3 (2013): 5-11. Print.