We search for three distinct polynomials with integer coefficients such that the product of any two members of the set added with their sum and increased by a non-zero integer (or polynomial with integer coefficients) is a perfect square.

Periodical:

The Bulletin of Society for Mathematical Services and Standards (Volume 10)

Pages:

1-6

Citation:

M.A. Gopalan et al., "DIO 3 - Tuples for Special Numbers - I", The Bulletin of Society for Mathematical Services and Standards, Vol. 10, pp. 1-6, 2014

Online since:

June 2014

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Open Access

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Creative Commons Attribution 4.0 International License

References:

A.F. Beardon and M.N. Deshpande (2007), Diophantine triples, The mathematical Gazette, 86 (2002), 258- 260.

Bugeaud, A. Dujella and M. Mignotte (2007), On the family of Diophantine triples , Glasgow Math.J., 49, 333-344.

Lj. Bacic, A. Filipin (2013), On the family of D(4)- triples , Bull. Belg. MTH. Soc. Simon Stevin 20, 777- 787.

Lj. Bacic, A. Filipin (2013), On the extendibility of D(4)- pairs, Math. Commun. 18, 447 -456.

M.N. Deshpande (2002), One interesting family of Diophantine triplets, International J. Math. ed. Sci. Tech., 33, 253-256.

M.N. Deshpande (2003), Families of Diophantine triplets, Bulletin of the Marathwada Mathematical Society, 4, 19-21.

Y. Fujita (2008), The extensibility of Diophantine pairs , J. Number theory, 128, 322-353.

Y. Fujita, A. Togbe (2011), Uniqueness of the extension of the triple , Notes Number Theory Discrete Math. 17, 42-49.

M.A. Gopalan and V. Pandichelvi (June 2009), On the extensibility of the Diophantine triple involving Jacobsthal numbers , International journal of Mathematics & Application, 2 (1), 1-3.

M.A. Gopalan and G. Srividhya (2009), Diophantine Qudrapules for Fibonacci numbers with property D(1), Indian Journal of Mathematics and mathematical Sciences, 5 (2), 57-59.

M.A. Gopalan and G. Srividhya (2010), Diophantine Qudrapules for Pell numbers with property D(1), Antarctica Journal of Mathematics, 7(3), 357-362.

M.A. Gopalan and V. Pandichelvi (2011), Construction of the Diophantine triple involving Polygonal numbers, Impact J. Sci. Tech., 5(1), 7-11.

M.A. Gopalan and G. Srividhya (2012), Two special Diophantine Triples, Diophntus J. Math., 1(1), 23-37.

M.A. Gopalan, V. Sangeetha and Manju Somanath (2014), Construction of the Diophantine polygonal numbers, Sch. J. Eng. Tech. 2, 19 -22.

M.A. Gopalan, K. Geetha and Manju Somanath (2014), On special Diophantine Triple, Archimedes Journal of Mathematics, 4(1), 37-43.

L. Szalay, V. Ziegler (2013), On an S-unit variant of Diophantine m-tuples, Publ. Math. Debrecen 83, 97 -121.

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