On squares expressible as sum of consecutive squares

• Main Authors: Rumbaoa, Joefort Dale O., Torres, Adelquin G.
• Format: text
• Language: English
• Published: Animo Repository 1995
• Subjects: Square; Congruences and residues; Numbers, > Theory of; Numbers, Divisibility of
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16265
• Institution: De La Salle University

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.