How can an inverse of a modulo m be used to solve the congruence ax\equiv b(\bmod m) when gcd(a,m)=1.

permaneceerc

permaneceerc

Answered question

2021-05-12

How can an inverse of a modulo m be used to solve the congruence axb(bmodm) when gcd(a,m)=1.

Answer & Explanation

mhalmantus

mhalmantus

Skilled2021-05-14Added 105 answers

Given information:
axb(bmodm)
Calculation:
In order to solve the congruence, we need an inverse of a modulo m.
Here, gcd (a, m) = 1 that means greatest common factor of a and m is 1. So, aand mare prime numbers then an inverse of a modulo m exists. Once we have an inverse a of a modulo m, we can solve the congruence axb(bmodm) by multiplying both sides of the linear congruence by a.

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