Question 1194346
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Given Table:<table border = "1" cellpadding = "5"><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></table>
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Part (a)


From the table,
B = 1
Y = 24
E = 4


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Part (b)


Each number mentioned in part (a) will be plugged into the formula (5m+9) mod 26 to get the corresponding encrypted number.


For the letter B, we plug in m = 1
5m+9 = 5(1)+9 = 14
Mod this with 26 and we end up with 14, so no change happens.
In other words,
14/26 = 0 remainder 14


Therefore, the letter B gets encrypted to the number 14.


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For the letter Y, we plug in m = 24
5m+9 = 5(24)+9 = 129


Then we could say
129/26 = 4.96 approximately


So,
129 - 4*26 = 25


In short, 129/26 = 4 remainder 25


The letter Y gets encrypted to the number 25.


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For the letter E, we plug in m = 4
5m+9 = 5(4)+9 = 29
Then,
29 - 26 = 3


Therefore, 
29/26 = 1 remainder 3
The letter E encrypts to 3.


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Summary:
B ---> 14
Y ---> 25
E ---> 3


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Part (c)


Use the results of the previous part.


B maps to 14, which corresponds to the letter "O". Use the table above. 
Y maps to 25, which is the letter Z.
E maps to 3, which is the letter D.


B: remainder 14 ---> letter O
Y: remainder 25 ---> Z
E: remainder 3 ---> D


The message "BYE" encrypts to "OZD"
where that first item is the letter "O" and not the number zero.
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