On the power sums problem of bi-periodic Fibonacci and Lucas polynomials

Tingting Du; Li Wang; Tingting Du; Li Wang

doi:10.3934/math.2024379

AIMS Mathematics

2024, Volume 9, Issue 4: 7810-7818. doi: 10.3934/math.2024379

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On the power sums problem of bi-periodic Fibonacci and Lucas polynomials

Tingting Du ,
Li Wang ^,

Research Center for Number Theory and Its Application, Northwest University, Xi'an, Shaanxi 710127, China

Received: 13 December 2023 Revised: 25 January 2024 Accepted: 08 February 2024 Published: 23 February 2024
MSC : 11B39, 11B37

This paper mainly discussed the power sums of bi-periodic Fibonacci and Lucas polynomials. In addition, we generalized these results to obtain several congruences involving the divisible properties of bi-periodic Fibonacci and Lucas polynomials.
- bi-periodic Fibonacci polynomial,
- bi-periodic Lucas polynomal,
- power sum,
- divisible property
Citation: Tingting Du, Li Wang. On the power sums problem of bi-periodic Fibonacci and Lucas polynomials[J]. AIMS Mathematics, 2024, 9(4): 7810-7818. doi: 10.3934/math.2024379

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Abstract

This paper mainly discussed the power sums of bi-periodic Fibonacci and Lucas polynomials. In addition, we generalized these results to obtain several congruences involving the divisible properties of bi-periodic Fibonacci and Lucas polynomials.

References

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