Luo, Miao; Tan, Qianrong; Wang, Shaofang There is no even primitive singular number of the form \(p^4qr\). (English) Zbl 1265.11009 J. Sichuan Univ., Nat. Sci. Ed. 49, No. 3, 511-513 (2012). Summary: In 2006, S. F. Hong et al. [Algebra Colloq. 13, No. 4, 689–704 (2006; Zbl 1140.11319)] showed that there is no even primitive singular number of the forms \(pqr\) and \(p^2qr\), and 270 and 520 are the all even primitive singular numbers of the form \(p^3qr\). In this paper, the authors show that there is no even singular number of the form \(p^4qr\), where \(p,\;q\) and \(r\) are distinct primes. MSC: 11A25 Arithmetic functions; related numbers; inversion formulas 11C20 Matrices, determinants in number theory Keywords:singular number; primitive singular number; even primitive singular number Citations:Zbl 1140.11319 PDFBibTeX XMLCite \textit{M. Luo} et al., J. Sichuan Univ., Nat. Sci. Ed. 49, No. 3, 511--513 (2012; Zbl 1265.11009) Full Text: DOI