# MUIC Math

Mathematics at MUIC

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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 2019/02/10 08:52 chatchawan 2019/02/02 11:12 chatchawan 2019/02/02 11:12 chatchawan created 2019/02/10 08:52 chatchawan 2019/02/02 11:12 chatchawan 2019/02/02 11:12 chatchawan created Last revision Both sides next revision Line 1: Line 1: - ====== p-adic valuation of Lucas sequences ====== + ====== ​$p$-adic valuation of Lucas sequences ====== ~~NOTOC~~ ~~NOTOC~~ Line 6: Line 6: 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. ​