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SUMMARY:Concatenations of distinct repdigits in various linear recurrence 
 sequences [MPIM]
DTSTART:20251015T123000Z
DTEND:20251015T133000Z
DTSTAMP:20260420T161500Z
UID:indico-event-665@math-events.uni-bonn.de
DESCRIPTION:Speakers: Mahadi Ddamulira (Makerere University/MPIM)\n\nNumbe
 r theory lunch seminar\nA repdigit is a natural number composed of repeate
 d instances of the same digit in its decimal expansion\, such as $11$\, $5
 55$\, or $888888$. A palindrome is a natural number that reads the same fo
 rwards and backward\, such as $121$\, $3553$\, or $9009$. Given a set of p
 ositive integers $ U $\, one can ask about how many positive integers that
  are (palindromic) concatenations of distinct repdits belong to $ U $? Thi
 s question leads to studying special forms of exponential Diophantine equa
 tions involving terms of linear recurrence sequences and concatenations of
  distinct repdigits. In this talk\, I will survey recent results about thi
 s problem when $ U $ is the set of Perrin numbers\, Tribonacci numbers\, P
 adovan numbers\, Narayana numbers\, and Tribonacci-Lucas numbers. The proo
 fs of these results heavily employ Baker's theory for nonzero lower bounds
  for linear forms in logarithms of algebraic numbers\,  reduction techniq
 ues involving the theory of continued fractions\, and the reduced basis LL
 L algorithm. These results have been obtained in joint work with various c
 olleagues such as H. Batte\,  T. P. Chalebgwa\, P. Emong\, F. Luca\, and 
 G. I. Mirumbe. \n\nhttps://math-events.uni-bonn.de/event/665/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/665/
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