number-theory / Number Theory, Covering Systems

Erdős Problem #1188

Estimate the number $F(x)$ of minimal distinct covering systems whose moduli all lie in $[1, x]$. The candidate proof gives $\log\log F(x)/\log x \to 1$, i.e. $F(x) = \exp(x^{1+o(1)})$.

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number-theoryJul 13, 2026Significance 10/100Registry: lean verified

Erdős Problem #1188

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Estimate the number $F(x)$ of minimal distinct covering systems whose moduli all lie in $[1, x]$. The candidate proof gives $\log\log F(x)/\log x \to 1$, i.e. $F(x) = \exp(x^{1+o(1)})$.

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Estimate the number $F(x)$ of minimal distinct covering systems whose moduli all lie in $[1, x]$. The candidate proof gives $\log\log F(x)/\log x \to 1$, i.e. $F(x) = \exp(x^{1+o(1)})$.

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