My Math Forum converting multiples

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 January 29th, 2012, 05:16 PM #1 Member   Joined: Jan 2012 Posts: 40 Thanks: 0 converting multiples Say you have a group of equations like 5*7 and 11*31. Each of theses equations are -1 and +1 respectivly away from a multiple of 6. When multiplied they will always be equal to a number of the form 6n-1. Say I wanted to find out what times 6 equals the 6n part of that. So for instance 5*7=35, 6*6=36; 11*31=341 6*57=342.What I have discovered from playing around with the numbers is any time the multiples are two away from each other like 5*7 or 11*13 just converting to the nearest multiple of 6 is enough. For the case of 11*13 we would make them 12*12 and if I want that in 6n form I would divide by two and multiply by two to make 6*24. That stuff is preety easy and if there is a better way to do what I just did let me know so I dont have to divide and multiply. The real reason I opened this topic is for the other numbers. 11*31 for instance. If I take 11*31 and turn it into 12*30 then divide the 12 by 2 to get 6 and multiply the 30 by 2 to get 60 then subtract 12 from 30 to get 18 then divide 18 by 6 to get 3 and subtract 3 from 60 to get 57 I end up with 6*57=342. Hope I wasnt confusing just now. I am wondering if there is a more efficent method assuming that I do not want to calculate the orginal equation and add 1 then divide by 6. The reason that I do not want to solve the equations first is there are some large numbers to deal with and I only want the 6n conversion anyways.
 January 29th, 2012, 05:49 PM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: converting multiples I recommend using a computer if the numbers are too large to work with directly. PARI/GP, in my .sig below, is a good choice for this kind of work; to solve this particular problm you can type (for example) Code: 378782785241*3275342785\/6 where the first part is the number and the "\/6" gives you the n such that the number is 6n+1 or 6n-1, if such an n exists.
 January 30th, 2012, 10:31 AM #3 Member   Joined: Jan 2012 Posts: 40 Thanks: 0 Re: converting multiples This program really kicks. What does it mean after it produces a number and at the end it has [+++]?
 January 30th, 2012, 10:34 AM #4 Member   Joined: Jan 2012 Posts: 40 Thanks: 0 Re: converting multiples Also can it read from txt documents? Like if I had two really large numbers in two txt documents would it be able to read the numbers from the txt documents? If thats possible can it save results to a txt document? Im going to be going over the faq to try to find the awnsers. Thanks for the help.
January 30th, 2012, 01:15 PM   #5
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Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: converting multiples

Quote:
 Originally Posted by Tylerman This program really kicks. What does it mean after it produces a number and at the end it has [+++]?
I'm not sure, can you give some context?

Quote:
 Originally Posted by Tylerman Also can it read from txt documents? Like if I had two really large numbers in two txt documents would it be able to read the numbers from the txt documents? If thats possible can it save results to a txt document? Im going to be going over the faq to try to find the awnsers. Thanks for the help.
Yes. Just type read("filename.txt") and it will parse the entire file. If you have several numbers in a file you can either name them in the file
Code:
num1 = 12.3;
num2 = 10.11;
piApprox = 3.1416;
or you can use readvec to store each in a vector.

You can write to files with the write and write1 commands (the former appends a newline, the latter does not).

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