Find all solutions of the following linear congruences. Inverses (when required) may not be determined "by inspection", but rather must be calculated using the appropriate method with all work shown. 14x\equiv 6(\bmod 31)

preprekomW

preprekomW

Answered question

2021-04-16

Find all solutions of the following linear congruences. Inverses (when required) may not be determined "by inspection", but rather must be calculated using the appropriate method with all work shown.
14x6(bmod31)

Answer & Explanation

Brighton

Brighton

Skilled2021-04-18Added 103 answers

Step 1
Given:
14x6(bmod31)
Here a=14. b=6 and N=31
Also gcd(14,31)=1
Hence there can be only one value of x.
Since, gcd(a,N)=1, let us multiply by the inverse of "a" in order to solve the given linear congruence.
The inverse of a=14 is 20.
Step 2
Hence, 20×14=20×6(bmod31)
280x120(bmod31)
x120(bmod31)
x27(bmod31)
Therefore, x=27
Answer
The value of x is 27

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