[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 122: include(/home/shoeb/public_html/www.matholympiad.org.bd/forum/includes/phpbb-latex.php) [function.include]: failed to open stream: No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 122: include() [function.include]: Failed opening '/home/shoeb/public_html/www.matholympiad.org.bd/forum/includes/phpbb-latex.php' for inclusion (include_path='.:/opt/php53/lib/php')
[phpBB Debug] PHP Warning: in file [ROOT]/includes/session.php on line 1042: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3887)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 4786: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3887)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 4788: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3887)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 4789: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3887)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 4790: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3887)
BdMO Online Forum • View topic - Pretty Diophantine Equation

Pretty Diophantine Equation

For discussing Olympiad Level Number Theory problems
Facebook Twitter

Pretty Diophantine Equation

Post Number:#1  Unread postby Kazi_Zareer » Tue Dec 20, 2016 11:21 am

Find all pairs of integers $ (x,y)$, such that


\[ x^2 - 2009y + 2y^2 = 0

\]
We cannot solve our problems with the same thinking we used when we create them.
User avatar
Kazi_Zareer
 
Posts: 86
Joined: Thu Aug 20, 2015 7:11 pm
Location: Malibagh,Dhaka-1217

Re: Pretty Diophantine Equation

Post Number:#2  Unread postby ahmedittihad » Fri Jan 13, 2017 6:21 am

The only solution is $(21,28)$.
Frankly, my dear, I don't give a damn.
User avatar
ahmedittihad
 
Posts: 147
Joined: Mon Mar 28, 2016 6:21 pm

Re: Pretty Diophantine Equation

Post Number:#3  Unread postby dshasan » Mon Feb 27, 2017 7:14 pm

Note that the equation can be rewritten as $m_2^2 + 8n_3^2 = 41n_3$, where $x = 7\times 7\times 2\times m_2$ and $y = 7\times 7\times 2\times 2\times n_3$, which gives the only solution when $(m_2, n_3) = (6,4) \Rightarrow (x,y) = (588,784)$ :D


Last bumped by dshasan on Mon Feb 27, 2017 7:14 pm.
The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.

- Charles Caleb Colton
dshasan
 
Posts: 66
Joined: Fri Aug 14, 2015 6:32 pm
Location: Dhaka,Bangladesh


Share with your friends: Facebook Twitter

  • Similar topics
    Replies
    Views
    Author

Return to Number Theory

Who is online

Users browsing this forum: No registered users and 2 guests