Question

In the group $\\{1, 2, 3, 4, 5, 6\\}$ under multiplication modulo $7$, if $5x = 4$, then $x =$

• A. 5
• B. 4
• C. 3
• D. 6

Answer 1

Answer: (A)

5

Answer 2

$\\{1, 2, 3, 4, 5, 6\\}$ is a group under multiplication and 1 is the identity element
$\Rightarrow \, 5^{-1} =3$
Now, $5x=4$
$5^{-1} 5x = 5^{-1} 4 (mod 7) \Righatrrow x = 3.4$ (mod 7)
$\Rightarrow \, x=5 (mod \: 7)$