"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 _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l