Solve the linear congruence

$7x\equiv 13\left(\text{mod}19\right)$

Braxton Pugh
2021-02-19
Answered

Solve the linear congruence

$7x\equiv 13\left(\text{mod}19\right)$

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casincal

Answered 2021-02-20
Author has **82** answers

Calculation:

Since$7x\equiv 13\left(\text{mod}19\right)$

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)

Since

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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