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        riddles >> putnam exam (pure math) >> A Sequence
        
(Message started by: THUDandBLUNDER on Dec 6th, 2004, 7:18am)
Title: A Sequence
Post by THUDandBLUNDER on Dec 6th, 2004, 7:18am
Define a sequence {un} by u0 = u1 = u2 = 1, and thereafter by the condition that

          ( un                 un+1 )
det      (                                                                                         )  = n!
          ( un+2    un+3 )

[smiley=forall.gif] n [smiley=eqslantgtr.gif] 0. Show that un is an integer [smiley=forall.gif] n.  
Title: Re: A Sequence
Post by Barukh on Dec 8th, 2004, 6:41am
[smiley=square.gif][hide]
un = (n-1)un-2
[/hide][smiley=square.gif]
Title: Re: A Sequence
Post by THUDandBLUNDER on Dec 9th, 2004, 6:44pm

on 12/08/04 at 06:41:27, Barukh wrote:
[smiley=square.gif][hide]
un = (n+1)un-2
[/hide][smiley=square.gif]

Therefore u2 = 3u0   ???
Title: Re: A Sequence
Post by Barukh on Dec 9th, 2004, 11:19pm

on 12/09/04 at 18:44:24, THUDandBLUNDER wrote:
Therefore u2 = 3u0   ???

Sorry for the typo.  :o


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