Solve the following linear congruence: 17x congruence 3(mod 7)

generals336

generals336

Answered question

2021-01-24

Solve the following linear congruence: 17x congruence 3(mod 7)

Answer & Explanation

faldduE

faldduE

Skilled2021-01-25Added 109 answers

Step 1 
Consider the provided question, 
We have to solve: 17x3(mod7) 
17 divided by 7 yields a remainder of 3.
The above congruence is therefore written as, 
3x3(mod7) 
here my aim is doing coefficient of x to be 1. 
So, multiply both sides by 5. 
15x15(mod7) 
Now, when divide 15 by 7, we get the remainder 1. 
here in this case we divide in both the 15. 
1x1(mod7) 
Thus, x1(mod7) 
Step 2 
The above solution is also written as, 
The solution of 17x3(mod7) is, 
x1(mod7) 
It can be also written as, 
x=1+7k where, k = 0,1,2,3,...

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