On squares expressible as sum of consecutive squares - Rumbaoa, Joefort Dale O. (Animo Repository, 1995)
This paper mainly concerns itself with squares expressible as sum of consecutive squares. Let | be the set of all integers k for which there exists a square expressible as a sum of k consecutive squares. Some necessary conditions that k must satisfy in order to belong to the set | are given. Squares which are sums of k consecutive squares are found with the use of diophantine equations which can be reduced to Pell's equation. A discussion on finding solutions to Pell's equation when k is a perfect square and when k is not a perfect square is included. It was also shown that if k belongs to |,then there exist infinitely many squares that can be written as the sum of k consecutive squares if and only if k is not a perfect square.