Notes on Sums of Squares of Consecutive Odd Integers.
Purchase
Purchase Print Copy
| Format | List Price | Price | |
|---|---|---|---|
| Add to Cart | Paperback | $20.00 | $16.00 20% Web Discount |
| Format | List Price | Price | |
|---|---|---|---|
| Add to Cart | Paperback | $20.00 | $16.00 20% Web Discount |
In a recent series of papers published in Mathematics Magazine, Brother U. Alfred investigates the conditions under which the sum of the squares of N consecutive odd integers can be a square. He derives several theorems to eliminate many values of N, and finds solutions for other values. Eight numbers below 1000 (193, 564, 577, 601, 673, 724, 772, and 913) remain unsolved in his work. Also, there are 17 values in his table of solutions for which the solution exceeds 10 digits. In this Paper, the eight cases are resolved, and solutions are presented for the 17 cases, only one of which contains as many as 7 digits. A systematic procedure for finding these solutions is demonstrated. 7 pp. Refs.
This report is part of the RAND Corporation Paper series. The paper was a product of the RAND Corporation from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.
Our mission to help improve policy and decisionmaking through research and analysis is enabled through our core values of quality and objectivity and our unwavering commitment to the highest level of integrity and ethical behavior. To help ensure our research and analysis are rigorous, objective, and nonpartisan, we subject our research publications to a robust and exacting quality-assurance process; avoid both the appearance and reality of financial and other conflicts of interest through staff training, project screening, and a policy of mandatory disclosure; and pursue transparency in our research engagements through our commitment to the open publication of our research findings and recommendations, disclosure of the source of funding of published research, and policies to ensure intellectual independence. For more information, visit www.rand.org/about/research-integrity.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.