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Thursday, February 8, 2018 - 16:00 to 17:00
Seminar Room, SMS
Dr. Shanta Laishram
Indian Statistical Institute, Delhi
Powers in products of terms of Binary Recurrence Sequences

It is known that there are only finitely many perfect powers in non degenerate binary recurrencesequences. However explicitly finding them is an interesting and a difficult problem for binary recurrencesequences. A breakthrough result of Bugeaud, Mignotte and Siksek states that Fibonacci sequences$(F_n)_{n\geq 0}$ given by $F_0=0, F_1=1$ and $F_{n+2}=F_n+F_{n+1}$ for $n\geq 0$ are perfect powersonly for $F_0=0, F_1=1, F_2=1, F_6=8$ and $F_{12}=144$.In this talk, we the problem of finding perfect powers in products of terms of Recurrence Sequences. We show thatthere are only perfect powers and also give an explicit method to find them. We explicitly find the perfect powers in products of terms of some well known recurrence sequence including Fibonacci, Pell, Jacobsthal and Mersenne sequences and associated Lucas sequences. 

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