"Robert J. Chassell" wrote:
>
> Julia Thompson <[EMAIL PROTECTED]> wrote
>
> Base 10 has a minor advantage in divisibility tests that I don't
> think you get with any other possible base between 5 and 17. And
> unlike 5 and 17, it's not prime.
>
> What are the tests and the advantage? I don't know anything about
> this. Perhaps it will reconcile me to base 10!
In base N, to check to see if a number is divisible by N-1, just add the
digits, and if their sum is divisible by N-1, the number itself is. So
in base 10, if the sum of the digits of a number add up to 9 or 18 or
27, etc., the number is divisible by 9.
If N-1 is a square, a similar divisibility test will work on sqrt(N-1).
So if the sum of digits of a number in base 10 is divisible by 3, the
number itself is divisible by 3.
If you like having that nifty little extra divisibility test, your base
must be N^2+1 for some N. So 5, 10 and 17 all work as bases with that
feature.
Base 12 has easier divisibility tests for more numbers, though.
Julia
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