Problem 1072

../

---

Statement. For any prime $p$, let $f(p)$ be the least integer such that $f(p)!+1\equiv 0\pmod{p}$.

Is it true that there are infinitely many $p$ for which $f(p)=p-1$? Is it true that $f(p)/p\to 0$ for almost all $p$?

Status. Open.

Source. erdosproblems.com/1072, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #1072, https://www.erdosproblems.com/1072.

References.

• [Gu04] Guy, Richard K., Unsolved problems in number theory. Third edition, Problem Books in Mathematics, Springer, New York (2004), xviii+437 pp. The site's remark places both questions in problem A2. Library home: guy_2004_unsolved_problems_number_theory.
• [HaSu02] Hardy, G. E. and Subbarao, M. V., A modified problem of Pillai and some related questions. Amer. Math. Monthly (2002), 554-559.

Formalization. Statement in formal-conjectures.

Progress

Not yet compiled.

Known Results

Not yet compiled.

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.

• hardy_2002_modified_problem_pillai_related_questions
• hardy_2002_modified_problem_pillai_related_questions / problem_g
• guy_2004_unsolved_problems_number_theory