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

djeljenike 2021-01-13 Answered
Solve the following linea congruence: 17x congruence 3(mod 210)
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Expert Answer

krolaniaN
Answered 2021-01-14 Author has 86 answers

Step 1
Given:
17x3(mod210)
Therefore,
x=1713(mod210)
Find 171(mod210)
210=17×12+6
17=6×2+5
6=5×1+1
Trace the steps backward.
1=65
=6(176×2)
=3×617
=3(21017×12)17
=3×21036×1717
=3×21037×17
Thus, 171(mod210)=37(mod210)=173(mod210)
Step 2
Hence,
x1713(mod210)
1733(mod210)
519(mod210)
99(mod210)
Thus, x99(mod210)
Therefore, 17×99=16833(mod210)
Step 3
Result:
Thus, x99(mod210)
Therefore, 17×99=16833(mod210)

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