document.write( "Question 1137583: Find the remainder when 4^503 is divided by 255 \n" ); document.write( "
Algebra.Com's Answer #755459 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "      Observe that the sequence of exponents 998,990,... is an arithmetic\r\n" );
document.write( "      sequence with common difference -8, and smallest positive term 6.\r\n" );
document.write( "      \"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d=%22%22\"\r\n" );
document.write( "      \"998%2B%28n-1%29%28-8%29=%22%22\"\r\n" );
document.write( "      \"998-8n%2B8=%22%22\"\r\n" );
document.write( "      \"1006-8n%3E0\"\r\n" );
document.write( "      \"1006%3E8n\"\r\n" );
document.write( "      \"125.75%3En\"\r\n" );
document.write( "      The 125th term is \r\n" );
document.write( "      \"a%5B125%5D=998%2B%28125-1%29%28-8%29=6\"\r\n" );
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document.write( "\"%282%5E8-1%29%282%5E998%2B2%5E990%2B%22...%22%2B2%5E14%2B2%5E6%29%2B2%5E6=%22%22\"\r\n" );
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document.write( "\"%28256-1%29%282%5E998%2B2%5E990%2B%22...%22%2B2%5E14%2B2%5E6%29%2B64\"\r\n" );
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document.write( "\"255%282%5E998%2B2%5E990%2B%22...%22%2B2%5E14%2B2%5E6%29%2B64\"\r\n" );
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document.write( "So the remainder is 64.\r\n" );
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document.write( "Edwin
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