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.
See http://www.research.att.com/~njas/sequences/index.html for the Online Encyclopedia.
Reviewer: Tom M.Apostol (Pasadena)
MSC:
| 11D85 | Representation problems |
Software:
OEISReferences:
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