Here is a seemingly simple Problem:
I have two natural numbers n and m, n < m such that S1:= n +...+ m is a square and also S2:= n +...+ m + (m+1) is a square.
Problem a) : Find n and m. You find a solution by looking at my demonstration "Sequence Sums that are Squares".
Problem b) : Now here is the hard part: find a second solution (maybe with a Mathematica program?) or prove that no other solution exists.