document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=271955>Question 271955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Modular arithmetic ...\r<BR>\n" );
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document.write( "Find all possible replacements for n for which each congruence is true.\r<BR>\n" );
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document.write( "	 	a. 6 + n &#8801; 1 (mod 7) 	b. 3 - n &#8801; 4 (mod 7)\r<BR>\n" );
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document.write( "		c. 2n &#8801; 1 (mod 3) 	d. n/2 &#8801; 2 (mod 3)  (n/s is a fraction)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #199016 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=199016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Modular arithmetic ...<BR>\n" );
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document.write( "Comment:  The fact to remember is (mod n) means n is zero.<BR>\n" );
document.write( "So 1 (mod 5) = 6 = 11 = 16 = -4 = - 9<BR>\n" );
document.write( "5 in all these numbers is zero so 16 is just 1+3*zero = 1<BR>\n" );
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document.write( "Find all possible replacements for n for which each congruence is true. <BR>\n" );
document.write( "a. 6 + n &#8801; 1 (mod 7)<BR>\n" );
document.write( "7 is zero so add it to the 1 to get:<BR>\n" );
document.write( "6 + n = 8 (7)<BR>\n" );
document.write( "n = 2+7k where k is any integer<BR>\n" );
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document.write( "b. 3 - n = 4 (mod 7)<BR>\n" );
document.write( "Regular arithmetic applies so solve for \"n\":<BR>\n" );
document.write( "n = 3-4 = -1 (mod 7)<BR>\n" );
document.write( "n = -1+7 = 6 (mod 7)<BR>\n" );
document.write( "n = 6 + 7k where k is any integer \r<BR>\n" );
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document.write( "c. 2n &#8801; 1 (mod 3)<BR>\n" );
document.write( "3 is zero so add it to the 1 to get:<BR>\n" );
document.write( "2n = 4 (mod 3)<BR>\n" );
document.write( "Use regular arithmetic to get:<BR>\n" );
document.write( "n = 2 + 3k where k is any integer<BR>\n" );
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document.write( "d. n/2 &#8801; 2 (mod 3) (n/s is a fraction)<BR>\n" );
document.write( "Use regular arithmetic to get:<BR>\n" );
document.write( "n = 4 (mod 3<BR>\n" );
document.write( "n = 1 + 3k where k is any integer<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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