
The only solutions are , (0, 0), (1, 1), (5, 10), (6, 13), and (85, 645) (Guy 1994, p.147), corresponding to the nontrivial triangular square pyramidal numbers 1, 55, 91, 208335.Numbers which are simultaneously tetrahedral and square pyramidal satisfy the Diophantine equation
Beukers (1988) has studied the problem of finding solutions via integral points on an elliptic curve and found that the only solution is the trivial . REFERENCES:Anglin, W.S. "The Square Pyramid Puzzle." Amer. Math. Monthly 97,120124, 1990. Anglin, W.S. The Queen of Mathematics: An Introduction to Number Theory. Dordrecht, Netherlands: Kluwer, 1995. Baker, A. and Davenport, H. "The Equations and ." Quart J. Math. Ser. 2 20, 129137, 1969.Ball, W.W.R. and Coxeter, H.S.M. MathematicalRecreations and Essays, 13th ed. New York: Dover, p.59, 1987. Beukers, F. "On Oranges and Integral Points on Certain Plane Cubic Curves."Nieuw Arch. Wisk. 6, 203210, 1988. Conway, J.H. and Guy, R.K. TheBook of Numbers. New 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, 2nd 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 Solution of a Problem Posed by E.Lucas." NordiskMat. Tidskrift 34, 6572, 1952. Lucas, É. Question 1180. Nouv. Ann. Math. Ser. 2 14, 336, 1875. Lucas, É. Solution de Question 1180. Nouv. Ann. Math. Ser. 2 15,429432, 1877. Ma, D.G. "An Elementary Proof of the Solution 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 Anderson, J.T. Excursionsin Number Theory. New York: Dover, pp.77 and 152, 1988. Sloane, N.J.A. Sequence 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 Web Resource. https://ubraintvjp.com/SquarePyramidalNumber.html ubraintvjp.com Web ResourcesMathematica» The #1 tool for creating Demonstrations and anything technical.  ubraintvjp.comAlpha» Explore anything with the first computational knowledge engine.  ubraintvjp.com Demonstrations Project» Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.  Computerbasedmath.org» Join the initiative for modernizing math education.  Online Integral Calculator» Solve integrals with ubraintvjp.comAlpha.  Stepbystep Solutions» Walk through homework problems stepbystep from beginning to end. Hints help you try the next step on your own.  ubraintvjp.com Problem Generator» Unlimited random practice problems and answers with builtin Stepbystep solutions. Practice online or make a printable study sheet.  ubraintvjp.com Education Portal» Collection of teaching and learning tools built by ubraintvjp.com education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more.
See more: What Is A Primary Standard In Chemistry ? Primary Standard
 ubraintvjp.com Language» Knowledgebased programming for everyone. 
Contact the ubraintvjp.com Team  © 19992021 ubraintvjp.com Research, Inc.  Terms of Use 
