To find: The inverse for 210 modulo 13.

sibuzwaW

sibuzwaW

Answered question

2021-02-16

To find: The inverse for 210 modulo 13.

Answer & Explanation

pivonie8

pivonie8

Skilled2021-02-18Added 91 answers

Given information:
210 modulo 13
Calculation:
Step 1. 210=1316+2 and so 2=2101316.
Step 2. 13=26+1 and so 1=1326
Step 3. 6=16+0
Thus, GCD(210,13)=1
Substituting back through step 21
1=1326
=13(2101316)6 by step (1)
=132106+1396
=13972106
1=97136210
1=(6)210+9713
Thus, 210(6)=1(bmod13) by the definition of bmod, so -6 is an inverse for 210bmod13.
Conclusion:
-6 is an inverse for 210 modulo 13.

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