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UID:5678@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20230404T110000
DTEND;TZID=Europe/Paris:20230404T120000
DTSTAMP:20241120T200144Z
URL:https://www.i2m.univ-amu.fr/evenements/ernest-popoli-20230404/
SUMMARY:Pierre Popoli (IECL Univ. Lorraine): On the binary digits of n and 
 n^2
DESCRIPTION:Pierre Popoli: Let s(n) denote the sum of digits in the binary 
 expansion of the integer n. Hare\, Laishram and Stoll (2011) studied the n
 umber of odd integers such that s(n) = s(n^2) = k\, for a given positive i
 nteger k. The remaining cases that could not be treated by theses authors 
 were k = 9\, 10\, 11\, 14 or 15. In this talk\, I will present the results
  of our article on the cases k = 9\, 10 and 11 and the difficulties to set
 tle for the two remaining cases k = 14 and 15.\nA related problem is to st
 udy perfect squares of odd integers with four binary digits. Bennett\, Bug
 eaud and Mignotte (2012) proved that there are only finitely many solution
 s and conjectured that the set of solutions is composed of 13\, 15\, 47 an
 d 111. In the same paper\, we give an algorithm to find all solutions with
  fixed sum of digits value\, supporting this conjecture\, as well as show 
 related results for perfect squares of odd integers with five binary digit
 s.\nThis is joint work with Aloui\, Jamet\, Kaneko\, Kopecki and Stoll.
CATEGORIES:Séminaire,Ernest
LOCATION:I2M Luminy - Ancienne BU\, Salle Séminaire2 (RdC)\, 163 Avenue de
  Luminy\, 13009 Marseille\, France\, 
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, 1300
 9 Marseille\, France\, ;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - Ancienne B
 U\, Salle Séminaire2 (RdC):geo:0,0
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