document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194346>Question 1194346</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Math\r<BR>\n" );
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document.write( "Encrypt the message “BYE” using the encryption e equals left parenthesis 5 m plus 9 right parenthesis m o d space 26. The table of number equivalents of the letters is given below.\r<BR>\n" );
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document.write( "Letter\r<BR>\n" );
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document.write( "Equivalent\r<BR>\n" );
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document.write( "A\r<BR>\n" );
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document.write( "0\r<BR>\n" );
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document.write( "B\r<BR>\n" );
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document.write( "1\r<BR>\n" );
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document.write( "C\r<BR>\n" );
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document.write( "2\r<BR>\n" );
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document.write( "D\r<BR>\n" );
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document.write( "3\r<BR>\n" );
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document.write( "E\r<BR>\n" );
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document.write( "4\r<BR>\n" );
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document.write( "F\r<BR>\n" );
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document.write( "5\r<BR>\n" );
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document.write( "G\r<BR>\n" );
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document.write( "6\r<BR>\n" );
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document.write( "H\r<BR>\n" );
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document.write( "7\r<BR>\n" );
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document.write( "I\r<BR>\n" );
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document.write( "8\r<BR>\n" );
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document.write( "J\r<BR>\n" );
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document.write( "9\r<BR>\n" );
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document.write( "K\r<BR>\n" );
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document.write( "10\r<BR>\n" );
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document.write( "L\r<BR>\n" );
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document.write( "11\r<BR>\n" );
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document.write( "M\r<BR>\n" );
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document.write( "12\r<BR>\n" );
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document.write( "N\r<BR>\n" );
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document.write( "13\r<BR>\n" );
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document.write( "O\r<BR>\n" );
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document.write( "14\r<BR>\n" );
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document.write( "P\r<BR>\n" );
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document.write( "15\r<BR>\n" );
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document.write( "Q\r<BR>\n" );
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document.write( "16\r<BR>\n" );
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document.write( "R\r<BR>\n" );
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document.write( "17\r<BR>\n" );
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document.write( "S\r<BR>\n" );
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document.write( "18\r<BR>\n" );
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document.write( "T\r<BR>\n" );
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document.write( "19\r<BR>\n" );
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document.write( "U\r<BR>\n" );
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document.write( "20\r<BR>\n" );
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document.write( "V\r<BR>\n" );
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document.write( "21\r<BR>\n" );
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document.write( "W\r<BR>\n" );
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document.write( "22\r<BR>\n" );
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document.write( "X\r<BR>\n" );
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document.write( "23\r<BR>\n" );
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document.write( "Y\r<BR>\n" );
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document.write( "24\r<BR>\n" );
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document.write( "Z\r<BR>\n" );
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document.write( "25\r<BR>\n" );
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document.write( "a) Change BYE into its numerical equivalent.<BR>\n" );
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document.write( "b) Find the encrypted number value for each.\r<BR>\n" );
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document.write( "c) Change back to letters.<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 #826539 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=826539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Given Table:<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Letter</TD><TD >Numeric Equivalent</TD></tr><tr><TD >A</TD><TD >0</TD></tr><tr><TD >B</TD><TD >1</TD></tr><tr><TD >C</TD><TD >2</TD></tr><tr><TD >D</TD><TD >3</TD></tr><tr><TD >E</TD><TD >4</TD></tr><tr><TD >F</TD><TD >5</TD></tr><tr><TD >G</TD><TD >6</TD></tr><tr><TD >H</TD><TD >7</TD></tr><tr><TD >I</TD><TD >8</TD></tr><tr><TD >J</TD><TD >9</TD></tr><tr><TD >K</TD><TD >10</TD></tr><tr><TD >L</TD><TD >11</TD></tr><tr><TD >M</TD><TD >12</TD></tr><tr><TD >N</TD><TD >13</TD></tr><tr><TD >O</TD><TD >14</TD></tr><tr><TD >P</TD><TD >15</TD></tr><tr><TD >Q</TD><TD >16</TD></tr><tr><TD >R</TD><TD >17</TD></tr><tr><TD >S</TD><TD >18</TD></tr><tr><TD >T</TD><TD >19</TD></tr><tr><TD >U</TD><TD >20</TD></tr><tr><TD >V</TD><TD >21</TD></tr><tr><TD >W</TD><TD >22</TD></tr><tr><TD >X</TD><TD >23</TD></tr><tr><TD >Y</TD><TD >24</TD></tr><tr><TD >Z</TD><TD >25</TD></tr>\n" );
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document.write( "Part (a)\r<BR>\n" );
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document.write( "From the table,<BR>\n" );
document.write( "B = 1<BR>\n" );
document.write( "Y = 24<BR>\n" );
document.write( "E = 4\r<BR>\n" );
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document.write( "================================================\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "Each number mentioned in part (a) will be plugged into the formula (5m+9) mod 26 to get the corresponding encrypted number.\r<BR>\n" );
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document.write( "For the letter B, we plug in m = 1<BR>\n" );
document.write( "5m+9 = 5(1)+9 = 14<BR>\n" );
document.write( "Mod this with 26 and we end up with 14, so no change happens.<BR>\n" );
document.write( "In other words,<BR>\n" );
document.write( "14/26 = 0 remainder 14\r<BR>\n" );
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document.write( "Therefore, the letter B gets encrypted to the number 14.\r<BR>\n" );
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document.write( "For the letter Y, we plug in m = 24<BR>\n" );
document.write( "5m+9 = 5(24)+9 = 129\r<BR>\n" );
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document.write( "Then we could say<BR>\n" );
document.write( "129/26 = 4.96 approximately\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "129 - 4*26 = 25\r<BR>\n" );
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document.write( "In short, 129/26 = 4 remainder 25\r<BR>\n" );
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document.write( "The letter Y gets encrypted to the number 25.\r<BR>\n" );
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document.write( "For the letter E, we plug in m = 4<BR>\n" );
document.write( "5m+9 = 5(4)+9 = 29<BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "29 - 26 = 3\r<BR>\n" );
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document.write( "Therefore, <BR>\n" );
document.write( "29/26 = 1 remainder 3<BR>\n" );
document.write( "The letter E encrypts to 3.\r<BR>\n" );
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document.write( "Summary:<BR>\n" );
document.write( "B ---> 14<BR>\n" );
document.write( "Y ---> 25<BR>\n" );
document.write( "E ---> 3\r<BR>\n" );
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document.write( "================================================\r<BR>\n" );
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document.write( "Part (c)\r<BR>\n" );
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document.write( "Use the results of the previous part.\r<BR>\n" );
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document.write( "B maps to 14, which corresponds to the letter \"O\". Use the table above. <BR>\n" );
document.write( "Y maps to 25, which is the letter Z.<BR>\n" );
document.write( "E maps to 3, which is the letter D.\r<BR>\n" );
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document.write( "B: remainder 14 ---> letter O<BR>\n" );
document.write( "Y: remainder 25 ---> Z<BR>\n" );
document.write( "E: remainder 3 ---> D\r<BR>\n" );
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document.write( "The message \"BYE\" encrypts to \"OZD\"<BR>\n" );
document.write( "where that first item is the letter \"O\" and not the number zero.<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );