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On the Sum of Consecutive Squares

  • H. T. Freitag
  • G. M. Phillips

Abstract

We seek solutions of the Diophantine equation
$$ {\left( {n + 1} \right)^2} + {\left( {n + 2} \right)^2} + \cdots + {\left( {n + k} \right)^2} = {m^2} $$
(1)
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
$$ {n^2} + {\left( {n + 1} \right)^2} = {m^2}. $$
(2)

Keywords

Positive Integer Related Equation Number Theory Difference Equation Infinite Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • H. T. Freitag
  • G. M. Phillips

There are no affiliations available

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