document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=648576>Question 648576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the largest number which is the product of positive integers whose sum is 2005? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #406739 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=406739\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x and y be positive integers.\r<BR>\n" );
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document.write( "Then let x*y be maximized by  x+y = 2005\r<BR>\n" );
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document.write( "In general, the closer you get to a square, the larger the product will be. We can either use this fact, or we can make a table. I'll leave you to make a table if you want. Knowing that 2005 is odd, x and y can differ by at most one. \r<BR>\n" );
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document.write( "x + x+1 = 2005\r<BR>\n" );
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document.write( "2x = 2004\r<BR>\n" );
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document.write( "x = 1002\r<BR>\n" );
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document.write( "(1002+1) is the other. \r<BR>\n" );
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document.write( "Then 1002 and 1003 are the two integers.\r<BR>\n" );
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document.write( "Their product is 1005006. </SPAN>\n" );
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