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Pigeons will like it (Posted on 2010-03-08) Difficulty: 2 of 5
Prove analytically that for any nonnegative integer k there exists a power of 3, terminating with 0..001, i.e. a sequence of k zeroes followed by digit 1,
e.g. k=0==> 3^0=1, 3^4 =81;
k=1==> 3^20=3486784401,
k=2==> 3^100= 515377520732011331036461129765621272702107522001.
Bonus question: Show that replacing the number 3 by any odd number, not terminating by 5, leaves your proof valid.

No Solution Yet Submitted by Ady TZIDON    
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Question re: Adding zeros (full solution) Why p.w.l.i.?? Comment 2 of 2 |
(In reply to Adding zeros (full solution) by Jer)

Jer,

I  like your reasoning and appreciate your solution.

However, prior to publishing my solution- let me pose  this question:

Why pigeons will like it?

 

Ady


  Posted by Ady TZIDON on 2010-03-28 21:22:12
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