document.write( "Question 753997: What is the remainder when 4¹⁰⁰ is divided by 10?\r
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Algebra.Com's Answer #458766 by Edwin McCravy(20056)\"\" \"About 
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What is the remainder when 4100 is divided by 10?
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document.write( "41 = 4, its last (only) digit is 4.\r\n" );
document.write( "42 = 16, its last digit is 6.\r\n" );
document.write( "43 = 64, its last digit is 4.\r\n" );
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document.write( "since 4×4 = 16 and 4×6 = 24, the last digits go\r\n" );
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document.write( "4,6,4,6,4,6,...\r\n" );
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document.write( "The odd powers of 4 end in 4 and the even numbered powers of 4\r\n" );
document.write( "end in 6\r\n" );
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document.write( "The 100th power or 4 will be an even numbered term of that\r\n" );
document.write( "sequence so it will end in 6.\r\n" );
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document.write( "When a positive integer is divided by 10 the remainder is \r\n" );
document.write( "always the last digit.\r\n" );
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document.write( "Answer: 6\r\n" );
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\n" ); document.write( "For how many different positive integer values of d does (dn – 12)² = 0 have integer solutions?
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document.write( "These 6 values of d, since (dn - 12)² is 0 when and only when dn = 12\r\n" );
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document.write( " d  n  dn  (dn - 12)  (dn - 12)²\r\n" );
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document.write( " 1 12  12      0          0\r\n" );
document.write( " 2  6  12      0          0\r\n" );
document.write( " 3  4  12      0          0\r\n" );
document.write( " 4  3  12      0          0\r\n" );
document.write( " 6  2  12      0          0\r\n" );
document.write( "12  1  12      0          0\r\n" );
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document.write( "Answer: 6 values\r\n" );
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document.write( "Edwin
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