A Paley type partial difference set exists in an abelian group of odd order v exactly when v is a prime power congruent to 1 mod 4 or v = n^4 or 9n^4 for odd n > 1.
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Paley type partial difference sets in abelian groups
A Paley type partial difference set exists in an abelian group of odd order v exactly when v is a prime power congruent to 1 mod 4 or v = n^4 or 9n^4 for odd n > 1.