forum.virtualchallengemeets.com • View topic - APMO #1 2003

[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 379: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.tex): failed to open stream: No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 236: fputs() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 237: fclose() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 280: copy(c832477573c15aaf177fe9d73036dc3e.png): failed to open stream: No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 281: chmod(): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.tex): failed to open stream: No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 236: fputs() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 237: fclose() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 280: copy(c832477573c15aaf177fe9d73036dc3e.png): failed to open stream: No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 281: chmod(): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.tex): failed to open stream: No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 236: fputs() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 237: fclose() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 280: copy(c832477573c15aaf177fe9d73036dc3e.png): failed to open stream: No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 281: chmod(): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.tex): failed to open stream: No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 236: fputs() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 237: fclose() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 280: copy(c832477573c15aaf177fe9d73036dc3e.png): failed to open stream: No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 281: chmod(): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.tex): failed to open stream: No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 236: fputs() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 237: fclose() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 280: copy(c832477573c15aaf177fe9d73036dc3e.png): failed to open stream: No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 281: chmod(): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.tex): failed to open stream: No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 236: fputs() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 237: fclose() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 280: copy(c832477573c15aaf177fe9d73036dc3e.png): failed to open stream: No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 281: chmod(): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/c832477573c15aaf177fe9d73036dc3e.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 4688: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3823)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 4690: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3823)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 4691: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3823)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 4692: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3823)
forum.virtualchallengemeets.com • View topic - APMO #1 2003

Page 1 of 1

APMO #1 2003

Posted: Tue Apr 17, 2007 7:43 pm

by stupidityismygam

Let [unparseable or potentially dangerous latex formula] be real numbers such that the polynomial

[unparseable or potentially dangerous latex formula]

factorises into eight linear factors [unparseable or potentially dangerous latex formula], with [unparseable or potentially dangerous latex formula] for [unparseable or potentially dangerous latex formula] Determine all possible values of [unparseable or potentially dangerous latex formula]

Posted: Tue Apr 17, 2007 8:11 pm

by kashhustler

whaa...?
factorises?
is that a word?

Posted: Tue Apr 17, 2007 8:19 pm

by stupidityismygam

according to aops, yes (i copy and paste these)

Posted: Tue Apr 17, 2007 8:27 pm

by Kurt

It is????

HA! People poke fun of me all the time for saying that. It's much quicker than saying "doing the prime factorization". *Slaps Nathan around*

Posted: Tue Apr 17, 2007 8:34 pm

by stupidityismygam

factorises is specially used in Britain and the same as factorizes

(aka a British guy translated it)