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There is no even primitive singular number of the form \(p^4qr\). (English) Zbl 1265.11009

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

Citations:

Zbl 1140.11319
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