document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1116320>Question 1116320</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Calculate<BR>\n" );
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document.write( "9^563 mod907<BR>\n" );
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document.write( "Identify which one of the following options gives the correct solution for the above expression ?<BR>\n" );
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document.write( " 310<BR>\n" );
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document.write( " 520<BR>\n" );
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document.write( "630<BR>\n" );
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document.write( "493\r<BR>\n" );
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document.write( "My working:\r<BR>\n" );
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document.write( "9^563 mod 907\r<BR>\n" );
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document.write( "First I identified the exponents.\r<BR>\n" );
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document.write( "9^1 mod 907<BR>\n" );
document.write( "9^2 mod 907<BR>\n" );
document.write( "9^16 mod 907 <BR>\n" );
document.write( "9^32 mod 907 <BR>\n" );
document.write( "9^512 mod 907\r<BR>\n" );
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document.write( "(512+32+16+2+1=563)\r<BR>\n" );
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document.write( "9^1 mod 907=9<BR>\n" );
document.write( "9^2 mod 907=81<BR>\n" );
document.write( "9^16 mod 907 =669<BR>\n" );
document.write( "9^32 mod 907 =410<BR>\n" );
document.write( "9^512 mod 907=862\r<BR>\n" );
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document.write( "To show my working between 9^32 mod 907 and 9^512 mod 907\r<BR>\n" );
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document.write( "9^64 mod 907= 410^2 mod 907 =305<BR>\n" );
document.write( "9^128 mod 907=305^2 mod 907=511<BR>\n" );
document.write( "9^256 mod 907 =511^2 mod 907 = 812<BR>\n" );
document.write( "9^512 mod 907= 812^2 mod 907=862\r<BR>\n" );
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document.write( "But I am not sure what is the final step....<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 #731240 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52798)</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=731240\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "But I am not sure what is the final step....<BR>\n" );
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document.write( "The final steps are \r\n" );
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document.write( "    a)  9^563 mod907 = 8*81*669*410*862 mod907 = 153211811040 mod907.\r\n" );
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document.write( "    b)  153211811040/907 = 168921511.6\r\n" );
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document.write( "    c)  9^563 mod907 = 153211811040 - 907*168921511 = 573.\r\n" );
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document.write( "<U>Answer</U>.  9^563 mod907 = = 573.\r\n" );
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document.write( "I didn't check your numbers - I simply used them . . . \r<BR>\n" );
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