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        riddles >> easy >> divide by 3
        
(Message started by: BNC on Jan 14^th, 2003, 7:19am)

Title: divide by 3
Post by BNC on Jan 14^th, 2003, 7:19am

Prove that a number is divisible by 3 iff the sum of its digits is divisible by 3.

Title: Re: divide by 3
Post by towr on Jan 14^th, 2003, 9:31am

So
http://tcw2.ppsw.rug.nl/~towr/PHP/formula.php?formula=%5Csum_%7Bi%3D0%7D%5EN+a_i++%5Ccdot+10%5Ei+%5Cin+M_3+%7B%5Crm+%7Eiff%7E%7D+%5Csum_%7Bi%3D0%7D%5EN+a_i+%5Cin+M_3
where M₃ is of course the set of multiples of three..
And now to prove it..
(I just want to show off my formula generator)

Title: Re: divide by 3
Post by towr on Jan 14^th, 2003, 10:16am

I've got it :P
click here to see (link to the formula, since I can't hide it like normal text) (http://tcw2.ppsw.rug.nl/~towr/PHP/showformula.php?formula=%5Csum_%7Bi%3D0%7D%5EN+a_i%5Ccdot+10%5Ei%5Cequiv%5Csum_%7Bi%3D0%7D%5EN+a_i+%2B%5Csum_%7Bi%3D0%7D%5EN+a_i%5Ccdot+%2810%5Ei-1%29%5Cequiv%5Csum_%7Bi%3D0%7D%5EN+a_i+%2B+9%5Ccdot%5Csum_%7Bi%3D0%7D%5EN+%28a_i%5Ccdot%5Csum_%7Bj%3D0%7D%5E%7Bi-1%7D10%5Ej%29)