New Rule for Divisibility by 7
Date: 11/01/97 at 18:15:06 From: Anonymous Subject: A new seven's divisibility rule Hi, Dr. Math - Now since you're a big "math expert," you should know the 7's divisibility rule. You know, double the one's digit and subtract that from the first integer excluding the one's digit. Well I have another 7's rule which has never been created before and I have made up ALL BY MYSELF. You can look in any book, but you won't find it because I made it up. Here it is: Multiply the integer excluding the one's digit by 3, and then add the one's digit. If the resulting integer is divisible by 7, the first integer is divisible by 7, and the resulting integer will be either positive or negative depending on the first integer - i.e., 07 = 0 x 3, 0 + 7 = 7 and -07 = 0 x 3, 0 + -7 = -7. The other divisibility rule doesn't have that happen in some cases- i.e., 7 = 7-14 = -7. Last year in school, I presented it to a classroom of students and they all tried to prove it wrong. They failed. So officially, the new divisibility rule was named The Peterson Rule, but it was only official in our school. I was hoping that you'd have connections to professors, so that's why I'm e-mailing you. I'd appreciate it if you could pass the word on so it could be in books one day. This would really, really, really mean a lot to me. Thanks. Oh, and by the way, I'm 12 years old, my name's Torin Peterson, and it's not a joke.
Date: 11/05/97 at 11:15:46 From: Doctor Terrel Subject: Re: A new seven's divisibility rule Dear Torin, Of course, it's not a joke. I believe you, really. You've just done a very good job of what so few students do these days: THINK for themselves. I congratulate you. You remind me of myself when I was younger. One time I did some independent thinking and found some nice results. But then later I saw them in a book; my ideas were really old. However, and this the most important thing, I did it by myself first. It's not important that other people had found it out before me, but that I did my own thinking first. So as to your "new" rule, well, I knew it too. Some years ago I was playing around with divisibility rules for 7 and other numbers (like 13, 17, 19, primes mostly). I discovered that each had a "subtract" rule, but they also had an "add" rule. The subtract rules seemed to be the more famous and are in the books, but the add ones work just as well. Maybe you should write your own math book - really, I'm not joking - and include your new rule in it. In fact, because you've written it to Dr. Math, it's now in our archives. So you've taken the first step. By the way, can you find rules for 13, 17, 19, etc., both subtract and add styles? That would be a good project for you and impress all your friends. Write again to report your discoveries. Good luck, friend. -Doctor Terrel, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Date: 11/10/97 at 20:35:28 From: Anonymous Subject: Re: A new seven's divisibility rule Hi, Dr. Terrel, it's Torin again. Well, I'm working on the 13, 17, and 19 rules now, and I've found the addition rule for 19. The rule is: 1. Make the ones digit an independent integer and the rest of the digits an indepentent integer, i.e., 234 > 23,4 2. Double the old ones digit. 3. Add that to the other integer. 4. If it is divisible by 19, the starting integer is divisible by 19. You can keep going if you can't tell. 5. Example: 570 - 1. 57,0 2. 0(2) = 0 3. 57+0=57 4. It is, and 57 = 5 + 14 = 19 I hope I'll be getting more in the near future, but I just wanted to report in. Thanks for knowing I wasn't kidding and giving me new challenges to work on. I appreciate it. See ya!
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994-2013 The Math Forum