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15.79 (2002)

Solved

Does there exist a Hausdorff group topology on $\mathbb{Z}$ such that the sequence $\{2^n + 3^n\}$ converges to zero?

Contributor: I. V. Protasov

Progress

Yes, there does, as follows from Theorem 3 in (I. Z. Ruzsa, Proc. Conf. Number theory (Budapest, 1987). Vol. I: Elementary and analytic, Colloq. Math. Soc. János Bolyai, 51, North-Holland, Amsterdam, 1990, 473–504). Another solution is in (S. V. Skresanov, Siberian Math. J., 61, no. 3 (2020), 542–544).

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