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n = \pm 1^2 \pm 2^2 \pm 3^2 \pm ... \pm k^2

Source: 8th QEDMO problem 2 (15. 1. 2011) https://artofproblemsolving.com/community/c1512515_qedmo_200507

May 15, 2021
number theorySum of Squares

Problem Statement

Let nn be an integer. Show that a natural number kk can be found for which, the following applies with a suitable choice of signs: n=±12±22±32±...±k2n = \pm 1^2 \pm 2^2 \pm 3^2 \pm ... \pm k^2
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