id: 06124938
dt: j
an: 2013a.00548
au: Withers, Christopher S.; Nadarajah, Saralees
ti: A solution to weighted sums of squares as a square.
so: Int. J. Math. Educ. Sci. Technol. 43, No. 8, 1099-1108 (2012).
py: 2012
pu: Taylor \& Francis, Abingdon, Oxon
la: EN
cc: F60
ut: control theory; Diophantine integer equations; sums of squares
ci: 
li: doi:10.1080/0020739X.2012.662290
ab: Summary: For $n=1,2,{\ldots}$, we give a solution $(x_1,{\ldots},x_n, N)$
    to the Diophantine integer equation $\sum_{j=1}^n x_j^2 = N^2$. Our
    solution has $N$ of the form $n!$, in contrast to other solutions in
    the literature that are extensions of Euler’s solution for $N$, a sum
    of squares. More generally, for given $n$ and given integer weights
    $m_1, m_2, {\ldots},m_n$ we give a solution to $\sum_{j=1}^n m_jx_j^2 =
    N^2$. The weights may be positive or negative and are subject to some
    restrictions. Choosing weights $ \pm$ 1 gives a solution to the problem
    of finding integer vectors of the same length.
rv: