User Name Remember Me? Password

 Number Theory Number Theory Math Forum

 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 xł+ył+zł=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 (17299-25^3) = 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:
 Originally Posted by CRGreathouse Are the variables integers, positive integers, or nonnegative integers?
If x+y+z=43
xł+ył+zł=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  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:
 Originally Posted by karthikeyan.jp (25,11,7) is a solution.
It's the only one. June 7th, 2012, 03:41 PM #6 Senior Member   Joined: Apr 2010 Posts: 215 Thanks: 0 Re: diophantine equation xł = 17299-ył-zł xł < 17299 x < 26 So all x,y,z satisfy n < 26. Also, 3nł = 17299 n = 17.93 .. So at least one satisfies n>17. xł=17299-18ł-zł 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 1ł+5ł+7ł=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:
 Originally Posted by mathbalarka Maybe I got the solution:
I did post it above...  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:
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  Tags diophantine, equation Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post aSteve641 Number Theory 2 August 1st, 2011 06:27 AM Liu997 Number Theory 1 March 25th, 2010 10:13 AM momo Number Theory 5 March 3rd, 2009 03:05 PM duz Number Theory 8 November 7th, 2008 02:29 PM Dacu Algebra 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top      