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

ringearV 2021-02-25 Answered
Solve the following linear congruence: 17x congruence 3(mod 210)
You can still ask an expert for help

Want to know more about Congruence?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Isma Jimenez
Answered 2021-02-26 Author has 84 answers

Step 1 Given:
17x3(mod 210)
Therefore,
x1713(mod 210)
Find: 171(mod 210)
210=17×12+6
17=6×2+5
6=5×1+1
Trace the steps backward.
1=65
=6(1762)
=3617
=3(2101712)17
3210361717
32103717
Thus, 171(mod 210)=37(mod 210)=173(mod 210)
Step 2 Hence,
x1713(mod 210)
1733(mod 210)
519(mod 210)
99(mod 210)
Thus, x99(mod 210)
Therefore, 17×99=16833(mod 210)
Step 3 Result:
Thus, x99(mod 210)
Therefore, 17×99=16833(mod 210)

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more