document.write( "Question 1044530: Prove that 7^(2n)+16n-1 is divisible by 64 \n" ); document.write( "
Algebra.Com's Answer #659854 by Edwin McCravy(20056)\"\" \"About 
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document.write( "Here is a proof using the binomial theorem.\r\n" );
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document.write( "\"7%5E%282n%29%2B16n-1\"\r\n" );
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document.write( "Every term of the binomial expansion of (8-1)2n\r\n" );
document.write( "except the last two terms contain a factor of 8 to a power\r\n" );
document.write( "2 or greater and thus they are all divisible by 64.  So the\r\n" );
document.write( "above becomes upon writing out the first two and last two\r\n" );
document.write( "terms of the binomial expansion: \r\n" );
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document.write( "Simplifying and using the property of combinations C(2n,2n-1)=C(2n,1)=2n\r\n" );
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document.write( "The last two terms in the binomial expansion cancel with the \r\n" );
document.write( "16n-1, so all the remaining terms are divisible by 64.  Thus \r\n" );
document.write( "the theorem is proved.\r\n" );
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document.write( "Edwin
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