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Template:Sequence of the Day for February 25

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Intended for: February 25, 2012

Timetable

  • First draft entered by Alonso del Arte on November 24, 2011 based on remarks by Charles Greathouse and Artur Jasinski ✓
  • Draft reviewed by Daniel Forgues on February 22, 2016
  • Draft to be approved by January 25, 2012

Yesterday's SOTD * Tomorrow's SOTD

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A175607: Largest number
x
such that the greatest prime factor of
x 2  −  1
is the
n
th prime.
{ 3, 17, 161, 8749, 19601, 246401, 672281, ... }
For any prime
p
, there are finitely many
x
such that
x 2  −  1
has
p
as its largest prime factor. For every prime
p
, is there some
x
where the greatest prime factor of
x 2  −  1
is
p
? Yes, there is. As mentioned by Luca and Najman, this problem is closely related to the one in A002071.