document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205778>Question 1205778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I have shown my working for the question below, am I on the right track?\r<BR>\n" );
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document.write( "〖Simplify 10〗^241  mod(13) \r<BR>\n" );
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document.write( "Fermat’s Little Theorem states:<BR>\n" );
document.write( "a^(p-1)≡1mod(p)\r<BR>\n" );
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document.write( "Substitute:<BR>\n" );
document.write( "10^12≡1mod(13) \r<BR>\n" );
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document.write( "By our multiplication theorem we know that if<BR>\n" );
document.write( "10^12≡1mod(13) <BR>\n" );
document.write( "Then<BR>\n" );
document.write( "10^((12)A)≡(1)^A mod (13) \r<BR>\n" );
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document.write( "We want to get from a power of 12 up to around 241, and 12 x 20 = 240<BR>\n" );
document.write( "         10^(12)(20) ≡1^20 mod(13) <BR>\n" );
document.write( "  ≡1mod(13)\r<BR>\n" );
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document.write( "So what we have so far is<BR>\n" );
document.write( "10^241 mod(13)≡10^240×10^1 mod(13) <BR>\n" );
document.write( "                          ≡1×10mod(13) <BR>\n" );
document.write( "                          ≡10mod(13)\r<BR>\n" );
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document.write( "When 10^241is divided by 13, the remainder is 10 \r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842809 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52788)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=842809\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "Your logic and your reasoning are correct.\r<BR>\n" );
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document.write( "Your solution and your answer are correct.\r<BR>\n" );
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document.write( "Nice job.\r<BR>\n" );
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document.write( "My congratulations.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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