# Solve the following linear congruence: 17x congruence 3(mod 210)

Solve the following linear congruence:
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Step 1 Given:

Therefore,

Find:
$210=17×12+6$
$17=6×2+5$
$6=5×1+1$
Trace the steps backward.
$1=6-5$
$=6-\left(17-6\ast 2\right)$
$=3\ast 6-17$
$=3\left(210-17\ast 12\right)-17$
$3\ast 210-36\ast 17-17$
$3\ast 210-37\ast 17$
Thus,
Step 2 Hence,

Thus,
Therefore,
Step 3 Result:
Thus,
Therefore,