On squares expressible as sum of consecutive squares
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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | text |
| Language: | English |
| Published: |
Animo Repository
1995
|
| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/16265 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | De La Salle University |
| Language: | English |
| Summary: | 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. |
|---|