A Solution of Dudeney’s Round Table Problem for \(p^eq^f +1\)

A solution of Dudeney’s round table problem is given when \(n\) is as follows:

1. \(n = pq + 1\), where \(p\) and \(q\) are odd primes.
2. \(n = p^e + 1\), where \(p\) is an odd prime.
3. \(n = p^e q^f + 1\), where \(p\) and \(q\) are distinct odd primes satisfying \(p \geq 5\) and \(q \geq 11\), and \(e\) and \(f\) are natural numbers.