seminar:cp_p-adic_valuation_of_lucas_sequences

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seminar:cp_p-adic_valuation_of_lucas_sequences [2019/02/02 11:12] chatchawan created |
seminar:cp_p-adic_valuation_of_lucas_sequences [2019/02/02 11:12] chatchawan |
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- | ====== p-adic valuation of Lucas sequences ====== | + | ====== $p$-adic valuation of Lucas sequences ====== |

~~NOTOC~~ | ~~NOTOC~~ | ||

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Applied Mathematics, Mahidol University International College | Applied Mathematics, Mahidol University International College | ||

- | 16:00 - 17:00 Wednesday 6th February 2019, Room 1406, MUIC | + | 16:00 - 17:00 Wednesday, 6th February 2019, Room 1406, MUIC |

==== Abstract ==== | ==== Abstract ==== | ||

For relatively prime integers $P$ and $Q$, the Lucas sequence $(U_n)_{n\ge 0} = (U_n(P,Q))_{n\ge 0}$ is defined recursively by $U_0 = 0$, $U_1=1$, and $U_{n} = P\cdot U_{n-1}-Q\cdot U_{n-2}$ for $n\ge 2$. A recent work by Sanna has revealed an astounding formula for the powers of primes in the prime factorization of the Lucas sequence. Sanna's work is a generalization of the work by Lengyel who gave such formula only for the Fibonacci numbers which are the quintessential Lucas sequence with $a=1$ and $b=-1$. In this talk, I will discuss such formula and give applications which are recent joint work with Panraksa. | For relatively prime integers $P$ and $Q$, the Lucas sequence $(U_n)_{n\ge 0} = (U_n(P,Q))_{n\ge 0}$ is defined recursively by $U_0 = 0$, $U_1=1$, and $U_{n} = P\cdot U_{n-1}-Q\cdot U_{n-2}$ for $n\ge 2$. A recent work by Sanna has revealed an astounding formula for the powers of primes in the prime factorization of the Lucas sequence. Sanna's work is a generalization of the work by Lengyel who gave such formula only for the Fibonacci numbers which are the quintessential Lucas sequence with $a=1$ and $b=-1$. In this talk, I will discuss such formula and give applications which are recent joint work with Panraksa. | ||

Last modified: 2019/02/10 08:52