On the representations of \(xy+yz+zx\). (English) Zbl 0970.11011

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.


11D85 Representation problems


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[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)
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