document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198925>Question 1198925</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number 4^1000 - 1 is divisible by<BR>\n" );
document.write( "a) 4 b) 5 c) 7 d) 13 e) 19 </SPAN>\n" );
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document.write( "ANSWER: b) 5<br><BR>\n" );
document.write( "Look at the pattern of remainders when 4^n-1 is divided by 5:<br><BR>\n" );
document.write( "4^1-1 = 3; remainder when divided by 5 is 3<BR>\n" );
document.write( "4^2-1 = 15; remainder when divided by 5 is 0<BR>\n" );
document.write( "4^3-1 = 63; remainder when divided by 5 is 3<BR>\n" );
document.write( "4^4-1 = 255; remainder when divided by 5 is 0<br><BR>\n" );
document.write( "The pattern repeats forever; the remainder when 4^1000-1 is divided by 5 is 0.<br><BR>\n" );
document.write( "You can find the similar patterns of remainders when 4^n-1 is divided by 7, 13, or 19; the length of the repeating patterns is such that 4^1000-1 will not be divisible by any of those other answer choices.<br><BR>\n" );
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