On the Sum of Consecutive Squares

H. T. Freitag and G. M. Phillips

A chapter in Applications of Fibonacci Numbers, 1996, pp 137-142 from Springer

Abstract: Abstract We seek solutions of the Diophantine equation (1) $$ {\left( {n + 1} \right)^2} + {\left( {n + 2} \right)^2} + \cdots + {\left( {n + k} \right)^2} = {m^2} $$ for integers n, k and m, with n ≥ − 1 and with k and m positive and, in §3, we will also briefly consider the related equation where m 2 is replaced by m 3. When k = 1, (1) is trivial. For k = 2 we replace n by n − 1 and express (1) in the form (2) $$ {n^2} + {\left( {n + 1} \right)^2} = {m^2}. $$

Keywords: Positive Integer; Related Equation; Number Theory; Difference Equation; Infinite Number (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0223-7_12

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DOI: 10.1007/978-94-009-0223-7_12

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