Problem 913

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Statement. Are there infinitely many $n$ such that if

$$n(n+1) = \prod_i p_i^{k_i}$$

is the factorisation into distinct primes then all exponents $k_i$ are distinct?

Status. Open.

Source. erdosproblems.com/913, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #913, https://www.erdosproblems.com/913.

References.

• [Er82c] Erdős, P., Miscellaneous problems in number theory. Congr. Numer. (1982), 25-45, p. 28.

Formalization. Statement in formal-conjectures.

Progress

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Known Results

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Linked library material

These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.

• erdos_1982_miscellaneous_problems_number_theory
• erdos_1982_miscellaneous_problems_number_theory / remark_p28