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Question

The solution of: 8modx6mod14 is,

A
8,6
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B
6,14
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C
6,13
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D
8,14
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Solution

The correct option is C 6,13
Solution:-
8x6(mod 14)

gcd(8,14)=2 divides 6

To find solutions, we first solve

8x14y=6

By trial and error method, we find a solution

(x,y)=(6,3)

This means that x6(mod 14) is a solution

To the congruence 8x6(mod 14)

Incongruent solutions are,

x=6+(k×142);k=0,1

x=6,13

Hence option C is the answer.

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