Solve the linear congruence 7x=13(\bmod 19)

Yasmin

Yasmin

Answered question

2021-04-14

Solve the linear congruence 7x=13(bmod19)

Answer & Explanation

Tasneem Almond

Tasneem Almond

Skilled2021-04-16Added 91 answers

Given information:
7x=13(bmod19)
Calculation:
Since, 7x=13(bmod19)
In order to find an inverse of a modulo m, we look for a multiple of a that exceeds multiple of mby 1.
11.7=1(bmod19)
So, 11 is the inverse of 7 modulo 19.
Multiplying both sides by 11 shows that
11.7x=11.13(bmod19)
So, 77=1(bmod19) and 143=77(bmod19)
Conclusion:
The linear congruence of 7x=13(bmod19) is 71=1(bmod19) and 143=77(bmod19).

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