References

ON SOME DIOPHANTINE EQUATIONS RELATED TO SQUARE TRIANGULAR AND BALANCING NUMBERS


[1] A. Behera and G. K. Panda, On the square roots of triangular numbers, Fibonacci Quart. 37(2) (1999), 98-105.

[2] L. E. Dickson, History of the Theory of Numbers, Volume 2, Strechert, New York, 1971.

[3] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Fifth Edition, Oxford University Press, New York, 1979.

[4] D. Kalman and R. Mena, The Fibonacci numbers-exposed, Mathematics Magazine 76 (2003), 167-181.

[5] R. Keskin and B. Demirtürk, Solution of some Diophantine equations using generalized Fibonacci and Lucas sequences, Ars Combinatorica (accepted).

[6] J. B. Muskat, Generalized Fibonacci and Lucas sequences and rootfinding methods, Mathematics of Computation 61(203) (1993), 365-372.

[7] G. K. Panda and P. K. Ray, Cobalancing numbers and cobalancers, International Journal of Mathematics and Mathematical Sciences 8 (2005), 1189-1200.

[8] G. K. Panda, Some fascinating properties of balancing numbers, Fibonacci Numbers and their Applications 10 (2006).

[9] D. C. D. Potter, Triangular square numbers, The Mathematical Gazette 56(396) (1972), 109-110.

[10] S. Rabinowitz, Algorithmic Manipulation of Fibonacci Identities, Application of Fibonacci Numbers, Volume 6, Kluwer Academic Publ., Dordrect, The Netherlands, (1996), 389-408.

[11] P. Ribenboim, My Numbers, My Friends, Springer-Verlag, New York, Inc., 2000.

[12] M. R. Schroeder, Number Theory in Science and Communication, Springer, 2005.

[13] S. A. Shirali, Fun with Triangular Numbers, 2010,
http://www.mathcelebration.com/PDF/TriangleNumPDF.p df

[14] Stanford Math Circle, Sunday, May 9, 2010, Square-Triangular Numbers, Pell’s Equation and Continued Fractions,
http://math.standfor.edu/circle/Pell.pdf

[15] K. B. Subramaniam, A simple computation of square triangular numbers, International Journal of Mathematics Education in Science and Technology 23 (1992), 790-793.

[16] K. B. Subramaniam, A divisibility properties of square triangular numbers, International Journal of Mathematics Education in Science and Technology 26 (1995), 284-286.

[17] James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 2011.

[18] Z. Yosma and R. Keskin, Some new identities concerning generalized Fibonacci and Lucas numbers (submitted).