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Let sk(n) be the number of representations of n as a sum of k odd squares. We study the function s8k+1(n ), where n is any odd positive integer. Special cases of our results are s9(p ) = 1 16 s16(8p) and 1 17 s17(p ) = 1 32 s32(8p), where p is any odd prime.

An odd square as a sum of an odd number of odd squares