Problem 826

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Statement. Are there infinitely many $n$ such that, for all $k\geq 1$,

$$\tau(n+k)\ll k?$$

Status. Open.

Source. erdosproblems.com/826, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #826, https://www.erdosproblems.com/826.

References.

• [La26] C. F. Lau, On the number of prime factors of consecutive integers. arXiv:2604.15042 (2026).

Formalization. Statement in formal-conjectures.

Progress

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Known Results

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