Then, for any sets U and V, by the Chinese remainder theorem, the numbers that are quadratic resides modulo every prime in U and nonresidues modulo every prime in V form a periodic sequence, so by Dirichlet's theorem on primes in arithmetic progressions this number-theoretic graph has the extension property.
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It can be used to prove that the Erdős–Rényi model of random graphs, when applied to countably infinite graphs, always produces a unique graph, the Rado graph.