# Find the solution of congruence: x^43 -= 47 (mod 713)

Find the solution of congruence:
${x}^{43}\equiv 47\left(\text{mod}713\right)$
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Theodore Schwartz
Step 1
Given that ${x}^{43}\equiv 47\left(\text{mod}713\right)$
$⇒{x}^{43}-47$ is divisible by 713
Let
$713m={x}^{43}-47$
$⇒713m+47={x}^{43}$...(1)
Using trail method:
Let suppose x=70
For x=70,
(1)$⇒m=\frac{{x}^{43}-47}{713}$
For x=70, we have the value of m as a positive integer.
Step 2
Hence x=70 is the solution of this congruence.