I was trying to solve this question, If the number $413283P759387$ is divisible by $13$,then what is the value of $P$? and stumbled upon this solution.
$413283P759387 = 0$ mod $13$
$4132830000000 + P000000 + 759387 = 0$ mod $13$
$4132830000000 = 0$ mod $13$
$P000000 = P x 10^6 = P$ mod $13$
$759387 = 5$ mod $13$
$(0 + P + 5) = 0$ mod $13$
P = 8
$\frac{4132836759387}{13} = 317910673799$
Can anyone please explain why is the remainder always $P$?
