document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=620707>Question 620707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve: 73x is congruent to(the three line equal symbol) 115 (mod 971).\r<BR>\n" );
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document.write( "I know you can change this to (73x-115)/971, but I'm not sure how to solve the rest of this. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #390349 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=390349\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 73x = 1 (mod 971)\r<BR>\n" );
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document.write( "971 | (73x - 1)\r<BR>\n" );
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document.write( "971y = 73x - 1\r<BR>\n" );
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document.write( "-73x + 971y = -1\r<BR>\n" );
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document.write( "73x - 971y = 1\r<BR>\n" );
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document.write( "971 = 13*73 + 22 ----> 22 = 971 -13*73\r<BR>\n" );
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document.write( "73 = 3*22 + 7  ----> 7 = 73 - 3*22\r<BR>\n" );
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document.write( "22 = 3*7 + 1  ----> 1 = 22 - 3*7\r<BR>\n" );
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document.write( "1 = 22 - 3*7\r<BR>\n" );
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document.write( "1 = 22 - 3*(73 - 3*22)\r<BR>\n" );
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document.write( "1 = 22 - 3*73 + 9*22\r<BR>\n" );
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document.write( "1 = 971 -13*73 - 3*73 + 9*(971 - 13*73)\r<BR>\n" );
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document.write( "1 = 971 - 13*73 - 3*73 + 9*971 - 117*73\r<BR>\n" );
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document.write( "1 = 10*971 - 13*73 - 3*73 - 117*73\r<BR>\n" );
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document.write( "1 = 10*971 - 133*73\r<BR>\n" );
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document.write( "Since 1 = 10*971 - 133*73, this means that for 73x = 1 (mod 971), the solution is x = -133 = 838 (mod 971)\r<BR>\n" );
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document.write( "So \r<BR>\n" );
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document.write( "73x = 1 (mod 971)\r<BR>\n" );
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document.write( "73*838 = 1 (mod 971)\r<BR>\n" );
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document.write( "Now multiply both sides by 115\r<BR>\n" );
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document.write( "73*838 = 1 (mod 971)\r<BR>\n" );
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document.write( "115*73*838 = 115*1 (mod 971)\r<BR>\n" );
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document.write( "73*(115*838) = 115*1 (mod 971)\r<BR>\n" );
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document.write( "73*(115*838) = 115 (mod 971)\r<BR>\n" );
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document.write( "73*96370 = 115 (mod 971)\r<BR>\n" );
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document.write( "73*241 = 115 (mod 971)\r<BR>\n" );
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document.write( "So the solution for x in 73x = 115 (mod 971) is x = 241\r<BR>\n" );
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