Geodesic
On some properties of two simultaneous polygonal sequences
Journal of integer sequences, Tome 10 (2007) no. 10
This paper focuses on the properties of integers that are simultaneously representable as both $m$-gonal and $n$-gonal numbers. Employing hyperbolic geometry, we ascertain both lower and upper bounds on these numbers when there is a finite set of these integers. We then consider the fundamental class of solutions to a generalized Pell-Diophantine equation that relates to these integers, and derive a fast algorithm that can be used to generate them.
Classification : 11D09
Keywords: polygonal number, pell Diophantine equation, quadratic equation, fundamental class, generating function 
@article{JIS_2007__10_10_a4,
     author = {Su,  Joseph C.},
     title = {On some properties of two simultaneous polygonal sequences},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {10},
     zbl = {1174.11368},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_10_a4/}
}
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Su,  Joseph C. On some properties of two simultaneous polygonal sequences. Journal of integer sequences, Tome 10 (2007) no. 10. http://geodesic.mathdoc.fr/item/JIS_2007__10_10_a4/