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Problem 1072 — Erdős Problems

Problem 1072

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 $p$ ?

Source: erdosproblems.com/1072

Number theory

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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.
HaSu02: Hardy, G. E. and Subbarao, M. V., A modified problem of Pillai and some related questions. Amer. Math. Monthly (2002), 554-559.

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