A number theory problem from Mathematical Reflections

by XmL, Jul 4, 2014, 4:52 AM

Problem(MR5 2013 O.285):Let $ a_n $ be the sequence of integers defined as $ a_1 = 1 $ and $ a_{n+1}=2^{n}(2^{a_{n}}-1) $ for $ n\ge1 $. Prove that $ n! $ divides $ a_n $

A super long solution
This post has been edited 4 times. Last edited by XmL, Aug 12, 2014, 11:15 PM

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check the spelling of the last word. :P

by MathLearner01, Jul 4, 2014, 1:36 PM

Still an immature proof writer :)

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  • Good blog! I hope to see more posts here!

    by WizardMath, Feb 3, 2018, 6:57 PM

  • Thanks Harry Potter :D

    by XmL, Jul 30, 2014, 10:47 PM

  • Hey dude. Nice blog. I like your work.

    by gamjawon, Jul 30, 2014, 7:43 AM

  • Thanks...although most of the posts here won't be about geometry...rightnow I'm trying to improve my skills in other areas such as number theory and combo.

    by XmL, Jun 5, 2014, 1:11 AM

  • Hi Geometer,,nice blog..:D

    by vanu1996, Jun 4, 2014, 1:27 PM

  • Check your private massage :)

    by zabihpourmahdi, Jan 11, 2013, 5:34 PM

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