Let $r_s(n)$ denote the number of ways
to write $n$ as the sum of $s$ squares
of integers.
The paper determines $r_s(n)$
modulo $2s$ when $s$ is prime or a
power of 2. For general $s$ it gives
a congruence for $r_s(n)$ modulo
the highest power of 2 dividing $2s$.
congruences for the number of ways to
write an integer as the sum of a fixed
number of squares of integers
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