Conjecture: Let G be a finite additive abelian group with |G| odd. Then any subset A of G with |A|=n>2 can be written as a_1,…,a_n in such a way that all the sums a_1+a_2,a_2+a_3,…,a_n-1+a_n,a_n+a_1 are distinct.

Kourovka Notebook Problem 21.130

Conjecture: Let $G$ be a finite additive abelian group with $|G|$ odd. Then any subset $A$ of $G$ with $|A|=n>2$ can be written as $\{a_1,\ldots,a_n\}$ in such a way that all the sums $a_1+a_2,a_2+a_3,\ldots,a_{n-1}+a_n,a_n+a_1$ are distinct.

References

Primary source

Kourovka Notebook, issue 21

group-theory

InKourovka Notebook 21

Posted 1 month ago

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