Claims

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2005_07_18_filaseta_ford_konyagin_pomerance_yu: The theorem of Filaseta, Ford, Konyagin, Pomerance and Yu that distinct moduli from N to CN, with C below a slow power of N, leave nearly the trivial density uncovered, so no constant C works; refereed in J. Amer. Math. Soc.

2018_11_08_balister_bollobas_morris_sahasrabudhe_tiba: Theorem 5.1 of the Inventiones paper (2022), a second proof that distinct moduli in [n, Kn] with n at least an absolute M leave density at least some positive number depending on K uncovered, so no constant C works; refereed.

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