In the froup Z_12, find |a|, |b|, and |a+b|a=3, b=8

Question

In the froup $Z_{12}$ , find $| a |, | b |$ , and $| a + b |$
$a = 3, b = 8$

Answer 1

Consider the provided qustion,
If a $\in Z_{n}$ then $| a | = n / (g c d (a, n))$
here given $Z_{12}$ . So, $n = 12$
Given $a = 6, b = 2$
So, $a + b = 6 + 2 = 8$
$| a | = | 3 | = \frac{12}{gcd (3, 12)} = \frac{12}{3} = 4$
$| b | = | 8 | = \frac{12}{gcd (8, 12)} = \frac{12}{4} = 3$
$| a + b | = | 11 | = \frac{12}{gcd (11, 12)} = \frac{12}{1} = 12$

In the froup Z_12, find |a|, |b|, and |a+b|a=3, b=8

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