More \(Z\)—Cyclic Room Squares

This paper deals with the existence of \({Z}\)-cyclic Room squares of order \(2v\) (or of side \(2v-1\)) whenever \(2v-1 =\Pi_{i=1}^{n}p^{\alpha_i}\), ( \(p_i=2^{m_i}b_i+1\geq 7\) are distinct primes, \(b_i\) are odd, \(b_i > 1\), and \(\alpha_i\) are positive integers, \(i = 1, 2, \ldots, n\)), and includes some further results involving Fermat primes.