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We consider the values taken by $n\times n$ circulant determinants withinteger entries when $n$ is the product of two distinct odd primes $p,q$. Thesecorrespond to the integer group determinants for $\mathbb Z_{pq}$, the cyclicgroup of order $pq$. We show that $p^2$ and $q^2$ are not determinants (moregenerally we show that the classic necessary divisibility conditions are neversufficient when $n$ contains at least two odd primes). We obtain a completedescription of the integer group determinants for $\mathbb Z_{15}$ (thesmallest unresolved group) and partial results for general $n=3p.$

Integer circulant determinants of order 15