Question

Solve the linear congruence 7x -= 13(mod 19)

Congruence
ANSWERED
asked 2021-02-19
Solve the linear congruence
\(\displaystyle{7}{x}\equiv{13}{\left(\text{mod}{19}\right)}\)

Answers (1)

2021-02-20
Calculation:
Since \(\displaystyle{7}{x}\equiv{13}{\left(\text{mod}{19}\right)}\)
In order to find an inverse of a modulo m, we look for a multiple of a that exceeds multiple of m by 1.
11.7=1(mod 19)
So, 11 is the inverse of 7 modulo 19.
Multiplying both sides by 11 shows that
11.7x = 11.13(mod 19)
so, 77 = 1(mod 19) and 143 = 77(mod 19)
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