ajh@sdcsvax.UUCP (Alan Hu) (08/29/83)
Back in my old Junior High Math Team Days, I had rules for all the
numbers 1-16. (You had to do those problems fast!) Since someone
already gave the rule for 7, I think I'll give the rule for 13.
Note: I am not a number theoretician, and I make no claims as such.
I don't even know if I can prove this. I was given this rule, and
I accepted it on faith. It seems to work.
Divisibility by 13:
A number n is divisible by 13 iff the number
floor(n/10) + 4 * (n mod 10) is divisible by 13.
For example, take 160485
16048 + 4 * 5 = 16068
1606 + 4 * 8 = 1638
163 + 4 * 8 = 195
19 + 4 * 5 = 39 (If you can't tell by now, you're hopeless!)
3 + 4 * 9 = 39 (And you deserve to sit here and look at 39's
. . . forever. By the way, can any of you derive
a function to show which numbers won't reduce
by this method? You know the number must be small,
because 4 times the units digit must be greater
than 9 times the rest of the number.)
--Alan J. Hu
sdcsvax!ajh