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

Solve the following linear congruence: 17x congruence 3(mod 7)
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Step 1
Consider the provided question,
We have to solve: $17x\equiv 3\left(\text{mod}7\right)$
When divide 17 by 7, we get the remainder 3.
So, the above congruence is wtitten as,
$3x\equiv 3\left(\text{mod}7\right)$
here my aim is doing coefficient of x to be 1.
So, multiply both sides by 5.
$15x\equiv 15\left(\text{mod}7\right)$
Now, when divide 15 by 7, we get the remainder 1.
here in this case we divide in both the 15.
$1x\equiv 1\left(\text{mod}7\right)$
Thus, $x\equiv 1\left(\text{mod}7\right)$
Step 2
The above solution is also written as,
The solution of $17x\equiv 3\left(\text{mod}7\right)$ is,
$x\equiv 1\left(\text{mod}7\right)$
It can be also written as,
x=1+7k where, k = 0,1,2,3,...