Borwein, Jonathan; Choi, Kwok-Kwong Stephen On the representations of \(xy+yz+zx\). (English) Zbl 0970.11011 Exp. Math. 9, No. 1, 153-158 (2000). Neil Sloane’s Online Encyclopedia of Integer Sequences lists eighteen positive integers from 1 to 462 that are not of the form in the title with integers \(x,y,z\geq 1\) and states that probably the list is complete. The authors prove there is at most one more candidate and it must exceed \(10^{11}\). Moreover, this case is excluded if a certain \(L\)-function has no Siegel zero. See http://www.research.att.com/~njas/sequences/index.html for the Online Encyclopedia. Reviewer: Tom M.Apostol (Pasadena) Cited in 1 ReviewCited in 2 Documents MSC: 11D85 Representation problems Keywords:representation of integers; \(L\)-function; Siegel zero Software:OEIS PDF BibTeX XML Cite \textit{J. Borwein} and \textit{K.-K. S. Choi}, Exp. Math. 9, No. 1, 153--158 (2000; Zbl 0970.11011) Full Text: DOI EuDML References: [1] Borwein J. M., Pi and the AGM: A study in analytic number theory and computational complexity (1987) · Zbl 0611.10001 [2] Chen X. G., Acta Math. Sinica 41 (3) pp 577– (1998) [3] Chowla S., Quart. J. Math. 5 pp 304– (1934) · Zbl 0010.33705 [4] Crandall R. E., Experimental Math. 8 (4) pp 367– (1999) · Zbl 0949.11062 [5] Rose H. E., A course in number theory,, 2. ed. (1994) · Zbl 0818.11001 [6] Weinberger P. J., Acta Arith. 22 pp 117– (1973) [7] Zhu F. Z., Chinese Ann. Math. Ser. B 9 (1) pp 79– (1988) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.