document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113235>Question 113235</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you find by mod (100) the last two number of\r<BR>\n" );
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document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2006 ALIGN=MIDDLE  ALT=\"2%5E2006\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82408 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=82408\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find by mod (100) the last two number of\r<BR>\n" );
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document.write( "2^100\r<BR>\n" );
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document.write( "= 2^(10^2)\r<BR>\n" );
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document.write( "= [2^10]^2\r<BR>\n" );
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document.write( "= [1024]^2\r<BR>\n" );
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document.write( "= 24^2 (mod 100)\r<BR>\n" );
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document.write( "= 576 (mod 100)\r<BR>\n" );
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document.write( "= 76 (mod 100)\r<BR>\n" );
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document.write( "====================\r<BR>\n" );
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document.write( "and<BR>\n" );
document.write( "2^2006\r<BR>\n" );
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document.write( "2^100 = 76 (mod 100)<BR>\n" );
document.write( "2^200 = 5776 = 76 (mod 100)<BR>\n" );
document.write( "2^400 = 5776 (mod100) = 76 (mod 100)<BR>\n" );
document.write( "2^800 = 2^1600 = 76 (mod 100)<BR>\n" );
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document.write( "2^2006 = 2^1600*2^400*2^6 = 76*76*64 (mod 100)<BR>\n" );
document.write( "= 76*64 mod 100<BR>\n" );
document.write( "= 4864 mod 100<BR>\n" );
document.write( "= 64 mod 100<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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