document.write( "Question 252126: show that 3^2008+4^2009 can be written as product of two positive integers each of which is larger than 2009^182. \n" ); document.write( "

Algebra.Com's Answer #183923 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
Note: The tutor \"drk\" did not show that
\n" ); document.write( "3^2008[1 +3*(4/3)^2009] is the product of two integers. In fact
\n" ); document.write( "[1 +3*(4/3)^2009] is not an integer!!!\r
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\n" ); document.write( "\n" ); document.write( "show that 3^2008+4^2009 can be written as product of two positive integers each of which is larger than 2009^182.
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document.write( "We use the fact that\r\n" );
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document.write( "We let  and \r\n" );
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document.write( "Then\r\n" );
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document.write( "Substituting back for  and \r\n" );
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document.write( "So this is the product of two very large integers. So we have\r\n" );
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document.write( "shown the first part.\r\n" );
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document.write( "Now we only need to show that the smaller of these, which is\r\n" );
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document.write( "is greater than .\r\n" );
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document.write( "I have figured out how to do this yet, but I'm working on it.\r\n" );
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document.write( "If and when I get it then I'll post it here.\r\n" );
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document.write( "Edwin

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