Abstract
Polygonal numbers are nonnegative integers constructed geometrically from the regular polygons. The triangular numbers, or triangles, count the number of points in the triangular array
Imo propositionem pulcherrimam et maxime generalem nos primi deteximus: nempe omnem numerum vel esse triangulum vex ex duobus aut tribus triangulis compositum: esse quadratum vel ex duobus aut tribus aut quatuorquadratis compositum: esse pentagonum vel ex duobus, tribus, quatuor aut quinque pentagonis compositum; et sic deinceps in infinitum, in hexagonis, heptagonis polygonis quibuslibet, enuntianda videlicet pro numero angulorum generali et mirabili propostione. Ejus autem demonstrationem, quae ex multis varus et abstrusissimis numerorum mysteriis derivatur, hic apponere non licet....1
P. Fermat [39, page 303]
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© 1996 Springer Science+Business Media New York
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Nathanson, M.B. (1996). Sums of polygons. In: Additive Number Theory. Graduate Texts in Mathematics, vol 164. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3845-2_1
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DOI: https://doi.org/10.1007/978-1-4757-3845-2_1
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