A group of students are lining up after recess in an $$m\times m$$ square array, such that $$5$$ students are left out if the square array is as large as possible. If $$18$$ more students join the group, they will create a perfect $$n\times n$$ square array with no one left out. How many students were there originally? 
Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers