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

generals336 2021-01-24 Answered
Solve the following linear congruence: 17x congruence 3(mod 7)
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Expert Answer

faldduE
Answered 2021-01-25 Author has 109 answers
Step 1
Consider the provided question,
We have to solve: 17x3(mod7)
When divide 17 by 7, we get the remainder 3.
So, the above congruence is wtitten 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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