A group of students is arranged to form an $$m\times m$$ square array, which is as large as possible, and $$5$$ students are left out. 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