June 7th, 2012, 09:31 AM  #1 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  diophantine equation
Hello, solve: x+y+z=43 x³+y³+z³=17299 Thanks in advance. 
June 7th, 2012, 09:34 AM  #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: diophantine equation
Are the variables integers, positive integers, or nonnegative integers?

June 7th, 2012, 10:06 AM  #3 
Member Joined: May 2012 From: Chennai,India Posts: 67 Thanks: 0  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 (1729925^3) = cube root of 1674 = 11 (approx) cube root of (1674  11^3) = 343 = 7^3 
June 7th, 2012, 10:13 AM  #4  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: diophantine equation Quote:
x³+y³+z³=17299 And x,y,z belong to Then x,y,z=? Quote:
 
June 7th, 2012, 12:45 PM  #5  
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: diophantine equation Quote:
 
June 7th, 2012, 03:41 PM  #6 
Senior Member Joined: Apr 2010 Posts: 215 Thanks: 0  Re: diophantine equation
x³ = 17299y³z³ x³ < 17299 x < 26 So all x,y,z satisfy n < 26. Also, 3n³ = 17299 n = 17.93 .. So at least one satisfies n>17. x³=1729918³z³ So, at least one other satisfies n<22. To sum up, we have: x>17,y<22,z<26 Hope this helps! :) 
June 8th, 2012, 04:50 AM  #7 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: diophantine equation
Maybe I got the solution: Consider the triplet 1,5,7 1+5+7=13(the last digit is 3) and 1³+5³+7³=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 
June 8th, 2012, 06:15 AM  #8  
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: diophantine equation Quote:
 
June 8th, 2012, 11:53 AM  #9  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: diophantine equation Quote:
 

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