= Bose-Chowla Sidon construction
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{title2=$\{a\in\mathbb Z/(p^2-1):\theta^a-\theta\in\mathbb F_p\}$}
Choose a generator $\theta$ of the multiplicative group of the quadratic <finite field extension>. Its $p$ shifts $\theta+t$ define $p$ distinct exponents modulo $p^2-1$. Equality of two sums of exponents gives $(\theta+s)(\theta+t)=(\theta+u)(\theta+v)$. Since $1,\theta$ are independent over the prime field, $s+t=u+v$ and $st=uv$, so the unordered pairs coincide. Thus the exponents form a <Sidon set> in the cyclic group. Taking integer representatives preserves the Sidon property. Primes within $o(\sqrt N)$ below $\sqrt N$ give $\sqrt N-o(\sqrt N)$ representatives in an interval of length $N$.
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