number-theory / Elementary number theory

Cohen's 22 Conjectures on Cyclic Numbers

22 conjectures of Cohen about cyclic numbers (integers with $\gcd(n, \varphi(n)) = 1$) settled at once - 16 proved, 6 disproved - together with a complete resolution of a related OEIS problem on sequences whose running averages are Fibonacci numbers (Fried's Conjecture 2).

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number-theorySep 30, 2025Significance 6/100Registry: unreviewed

Cohen's 22 Conjectures on Cyclic Numbers

Prior state unknownproved

22 conjectures of Cohen about cyclic numbers (integers with $\gcd(n, \varphi(n)) = 1$) settled at once - 16 proved, 6 disproved - together with a complete resolution of a related OEIS problem on sequences whose running averages are Fibonacci numbers (Fried's Conjecture 2).

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22 conjectures of Cohen about cyclic numbers (integers with $\gcd(n, \varphi(n)) = 1$) settled at once - 16 proved, 6 disproved - together with a complete resolution of a related OEIS problem on sequences whose running averages are Fibonacci numbers (Fried's Conjecture 2).

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