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June 7th, 2012, 10:31 AM   #1
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diophantine equation

Hello,
solve:
x+y+z=43
x+y+z=17299
Thanks in advance.
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June 7th, 2012, 10:34 AM   #2
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Re: diophantine equation

Are the variables integers, positive integers, or nonnegative integers?
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June 7th, 2012, 11:06 AM   #3
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Re: diophantine equation

(25,11,7) is a solution..

i am still working on proving it.

cube root of 17299 = 25 (approx)
cube root of (17299-25^3) = cube root of 1674 = 11 (approx)
cube root of (1674 - 11^3) = 343 = 7^3

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June 7th, 2012, 11:13 AM   #4
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Re: diophantine equation

Quote:
Originally Posted by CRGreathouse
Are the variables integers, positive integers, or nonnegative integers?
If x+y+z=43
x+y+z=17299
And x,y,z belong to
Then x,y,z=?
Quote:
Originally Posted by karthikeyan.jp
(25,11,7) is a solution..

i am still working on proving it.

cube root of 17299 = 25 (approx)
cube root of (17299-25^3) = cube root of 1674 = 11 (approx)
cube root of (1674 - 11^3) = 343 = 7^3

I have done this too, but we both are iterating here, is there a proper diophantic non iterating method to solve it? However, thank you for the help
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June 7th, 2012, 01:45 PM   #5
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Re: diophantine equation

Quote:
Originally Posted by karthikeyan.jp
(25,11,7) is a solution.
It's the only one.
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June 7th, 2012, 04:41 PM   #6
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Re: diophantine equation

x = 17299-y-z
x < 17299
x < 26
So all x,y,z satisfy n < 26.

Also,
3n = 17299
n = 17.93 ..
So at least one satisfies n>17.

x=17299-18-z
So, at least one other satisfies n<22.

To sum up, we have:
x>17,y<22,z<26

Hope this helps! :)
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June 8th, 2012, 05:50 AM   #7
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Re: diophantine equation

Maybe I got the solution:
Consider the triplet 1,5,7
1+5+7=13(the last digit is 3) and 1+5+7=469(the last digit is 9)
so, we can assume that x=10a+1, y=10b+5, z=10c+7
It implies that a+b+c=3, and we are done
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June 8th, 2012, 07:15 AM   #8
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Re: diophantine equation

Quote:
Originally Posted by mathbalarka
Maybe I got the solution:
I did post it above...
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June 8th, 2012, 12:53 PM   #9
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Re: diophantine equation

Quote:
Originally Posted by CRGreathouse
Quote:
Originally Posted by mathbalarka
Maybe I got the solution:
I did post it above...
I got the method to find the solution
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