Vyacheslav M. Abramov
Published 2025-04-27, updated 2025-05-07Version 3
Paul Erdos posed the following question: Is there a prime number $p>5$ such that the residues of $2!$, $3!$,\ldots, $(p-1)!$ modulo $p$ all are distinct? In this short note, we prove that there are no such prime numbers.
Comments: Dear readers, I need to withdraw this paper since I was shown a counterexample. At this moment I cannot fix an error. I shall return to this question as soon as I find a solution
Several new relations for the $n^{th}$ prime number
Prime numbers in logarithmic intervals
Two statements that are equivalent to a conjecture related to the distribution of prime numbers
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