On a problem of Recaman and its generalization
Let \(k>1\) be an integer and denote by \(\varphi(k)\) Euler's function. We say that \(k\) is a \(P\)-integer if the first \(\varphi(k)\) primes coprime to \(k\) form a reduced residue system modulo \(k\). The authors prove that the only prime \(P\)-integer is \(2\). Let \(k>1\) be an integer with the least prime divisor \(>\log k\). Then \(k\) is a \(P\)-integer if and only if \(k\in\{2,4,6\}\). Let \(k\) be the product of the primes \(\leq x\) for some \(x\geq 2\). Then \(k\) is a \(P\)-integer if and only if \(k\in\{2,6,30\}\).
scientific article; zbMATH DE number 5817562