
The just solutions room , (0, 0), (1, 1), (5, 10), (6, 13), and also (85, 645) (Guy 1994, p.147), equivalent to the nontrivial triangle square pyramidal numbers 1, 55, 91, 208335.Numbers which are concurrently tetrahedral and square pyramidal fulfill the Diophantine equation
Beukers (1988) has actually studied the problem of finding remedies via integral points on one elliptic curve and also found that the just solution is the trivial . REFERENCES:Anglin, W.S. "The Square Pyramid Puzzle." Amer. Math. Monthly 97,120124, 1990. Anglin, W.S. The Queen the Mathematics: An arrival to Number Theory. Dordrecht, Netherlands: Kluwer, 1995. Baker, A. And also Davenport, H. "The Equations and also ." Quart J. Math. Ser. 2 20, 129137, 1969.Ball, W.W.R. And Coxeter, H.S.M. MathematicalRecreations and also Essays, 13th ed. Brandnew York: Dover, p.59, 1987. Beukers, F. "On Oranges and Integral clues on certain Plane Cubic Curves."Nieuw Arch. Wisk. 6, 203210, 1988. Conway, J.H. And Guy, R.K. TheBook the Numbers. Brandnew York: SpringerVerlag, pp.4750, 1996. Dickson, L.E. History of the theory of Numbers, Vol.2: Diophantine Analysis. New York: Dover, 2005. Guy, R.K. "Figurate Numbers." §D3 in Unsolved problems in Number Theory, second ed. New York: SpringerVerlag, pp.147150, 1994. Kanagasabapathy, P. And Ponnudurai, T. "The simultaneous Diophantine Equations and ." Quart. J. Math. Ser. 2 26, 275278, 1975.Ljunggren, W. "New systems of a trouble Posed through E.Lucas." NordiskMat. Tidskrift 34, 6572, 1952. Lucas, É. Inquiry 1180. Nouv. Ann. Math. Ser. 2 14, 336, 1875. Lucas, É. Equipment de concern 1180. Nouv. Ann. Math. Ser. 2 15,429432, 1877. Ma, D.G. "An Elementary proof of the systems to the Diophantine Equation ." Sichuan Daxue Xuebao 4, 107116, 1985.MoretBlanc, M. Question 1180. Nouv. Ann. Math. Ser. 2 15, 4648, 1876. Ogilvy, C.S. And also Anderson, J.T. Excursionsin Number Theory. New York: Dover, pp.77 and 152, 1988. Sloane, N.J.A. Succession A000330/M3844in "The OnLine Encyclopedia of integer Sequences." Watson, G.N. "The problem of the Square Pyramid." Messenger. Math. 48,122, 1918. Wolf, T. "The Puzzle." http://home.tiscalinet.ch/t_wolf/tw/misc/squares.html. Referenced on ubraintvjp.comAlpha: Square Pyramidal Number CITE THIS AS:Weisstein, Eric W. "Square Pyramidal Number."From ubraintvjp.comA ubraintvjp.com net Resource. Https://ubraintvjp.com/SquarePyramidalNumber.html ubraintvjp.com web ResourcesMathematica» The #1 device for developing Demonstrations and also anything technical.  ubraintvjp.comAlpha» Explore anything through the an initial computational understanding engine.  ubraintvjp.com Demonstrations Project» Explore thousands of totally free applications across science, mathematics, engineering, technology, business, art, finance, society sciences, and also more.  Computerbasedmath.org» Join the initiative because that modernizing mathematics education.  Online Integral Calculator» Solve integrals v ubraintvjp.comAlpha.  Stepbystep Solutions» Walk through homework difficulties stepbystep from beginning to end. Hints assist you try the following step on her own.  ubraintvjp.com difficulty Generator» Unlimited random exercise problems and also answers with builtin Stepbystep solutions. Practice online or make a printable research sheet.  ubraintvjp.com education and learning Portal» Collection of teaching and also learning tools constructed by ubraintvjp.com education experts: dynamic textbook, class plans, widgets, interaction Demonstrations, and more.
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