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Powers often in other bases. (Posted on 2013-04-07) Difficulty: 3 of 5
Create a table of powers of 10 in binary starting with 101 = 10102 then create a similar table in base 5 starting with 101 = 205.

If you look at the lengths of the numbers in the two tables combined, prove there is exactly one each of length 2, 3, 4...

No Solution Yet Submitted by Jer    
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Some Thoughts re: further hint -just waiting. Comment 3 of 3 |
(In reply to further hint by Charlie)

I've started  with compiling log(10,2)+1 and log(10,5)+1 to

see how the number of digit progresses, (4,7,10,14...etc-)

and got the idea, how it works....but that ,as you have mentioned,-    is not a proof.

Anxious to see the formal proof re z+1/z for increasing powers of z.

  Posted by Ady TZIDON on 2013-04-07 21:36:27
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