Abstract
SummaryThis note shows that with the exception of (5 × 2k)2, an integer square can be written as sums of 2, 3, and 4 positive squares if and only if it has at least one prime factor congruent to 1 mod 4. Moreover such a square n can be written as a sum of k positive squares for all k from 1 to n - 14. The question of when a non-square can be written as a sum of k positive squares is also examined.
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