lwfrgin

2021-03-05

Find the solution of congruence:

${x}^{43}\equiv 47\left(\text{mod}713\right)$

Theodore Schwartz

Skilled2021-03-06Added 99 answers

Step 1

Given that${x}^{43}\equiv 47\left(\text{mod}713\right)$

$\Rightarrow {x}^{43}-47$ is divisible by 713

Let

$713m={x}^{43}-47$

$\Rightarrow 713m+47={x}^{43}$ ...(1)

Using trail method:

Let suppose x=70

For x=70,

(1)$\Rightarrow m=\frac{{x}^{43}-47}{713}$

For x=70, we have the value of m as a positive integer.

Step 2

Hence x=70 is the solution of this congruence.

Given that

Let

Using trail method:

Let suppose x=70

For x=70,

(1)

For x=70, we have the value of m as a positive integer.

Step 2

Hence x=70 is the solution of this congruence.

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