Topic Content:
- Questions & Solutions – Modular Arithmetic
Example 6.3.1:
From the multiplication table for arithmetic (mod 6) find the following:
(i) \(\scriptsize 2 \bigotimes x = 3 \)
(ii) \(\scriptsize 5 \bigotimes x = 1 \)
(iii) \(\scriptsize 0 ⨸ 3 \)
(iv) \(\scriptsize 2 ⨸ 5 \)
Solution
(i) \(\scriptsize 2 \bigotimes x = 3 \)
For \( \scriptsize 2 \: \bigotimes \: x = 3\)
From the table, x does not exist.
(ii) \( \scriptsize 5 \: \bigotimes \: x = 1 \)
For \( \scriptsize 5 \: \bigotimes \: x = 1 \)
From the table, x = 5
(iii) \(\scriptsize 0 ⨸ 3 \)
Let 0 ⨸ 3 = p
i.e. 3p = 0 (mod 6)
From the table, p = 0, 2 and 4
(iv) \(\scriptsize 2 ⨸ 5 \)
Let 2 ⨸ 5 = p
i.e. Â 5p = 2 (mod 6)
From the table p = 4
Example 6.3.2:
Find the value(s) of the following:
(i) \( \scriptsize 7 \: \bigotimes \: 9^{-1} \: (mod \:17) \)
(ii) \( \scriptsize 20 \: ⨸ \: 8 \: (mod \:12) \)
(iii) \( \scriptsize 1 \: ⨸ \: 2 \: (mod \:4) \)
(iv) \( \scriptsize 98 \: ⨸ \: 10 \: (mod \:6) \)
Solution
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PLS CAN SOMEBODY HELP ME EXPLAIN EX 1 iii & iv???????????????