Create a table of powers of 10 in binary starting with 10

^{1} = 1010

_{2} then create a similar table in base 5 starting with 10

^{1} = 20

_{5}.

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...

(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.**