Eleanor is trying to solve a modular congruence that Dr Critz has written up on the blackboard:

$36$x$63($mod$219).$

First, Eleanor writes the solution as an integer x with respect to a smallest possible modulus k :

x$($modk$).$

Next, Eleanor writes the solution as a set of integers $\{$x$1,$x$2,...\}$ with respect to the original modulus $219$ :

x in $($mod$219).$