document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192797>Question 1192797</A>: <I><SPAN STYLE=\"word-break: break-all;\"> MAT 145: Topics In Contemporary Math<BR>\n" );
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document.write( "     More Modular Arithmetic\r<BR>\n" );
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document.write( "Find each of the following.\r<BR>\n" );
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document.write( "10) (5 * 11) mod 4 \r<BR>\n" );
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document.write( "11) (31 * 14) mod 7 \r<BR>\n" );
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document.write( "12) (15 * 4) mod 9\r<BR>\n" );
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document.write( "You can work this kind of problem mod n by doing the indicated multiplications and evaluating the products mod n.<br><BR>\n" );
document.write( "10) (5*11) mod 4 = (55) mod 4; 55/4 = 12 remainder 3 --> answer: 3<BR>\n" );
document.write( "11) (31*14) mod 7 = (434) mod 7; 434/7 = 62 remainder 0 --> answer: 0<BR>\n" );
document.write( "12) (15*4) mod 9 = (60) mod 9; 60/9 = 6 remainder 6 -- answer: 6<br><BR>\n" );
document.write( "I suspect if this is a learning exercise in modular arithmetic that you were expected to use the features of modular arithmetic, as follows.<br><BR>\n" );
document.write( "10) (5*11) mod 4 = (5) mod 4 * (11) mod 4 = 1*3=3<BR>\n" );
document.write( "11) (31*14) mod 7 = (31) mod 7 * (14) mod 7 = 3*0 = 0<BR>\n" );
document.write( "12) (15*4) mod 9 = (15) mod 9 + (4) mod 9 = (6*4) mod 9 = (24) mod 9 = 6<br><BR>\n" );
document.write( "In these examples, working the problems this second way is a bit easier; in example 11 it makes the work very simple.<br><BR>\n" );
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