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  Far East Journal of Mathematical Sciences (FJMS)  
 ISSN: 0972-0871
 
 
 

     Far East Journal of Mathematical Sciences (FJMS)
    Volume 33, Issue 3, Pages 267 - 275 (June 2009)


A NOTE ON THE ABC-CONJECTURE

R. A. Mollin (Canada)

Received February 6, 2009

References:



[1] E. Bombieri, Roth’s theorem and the abc-conjecture, ETH Zürich, 1994, preprint.

[2] R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, New York, Berlin, 2001.

[3] N. D. Elkies, ABC implies Mordell, Indagationes Math. 11 (2000), 197-200.

[4] P. Erdös, How many pairs of products of consecutive integers have the same prime factors?, Amer. Math. Monthly 87 (1980), 391-392.

[5] G. Faltings, Diophantine approximation on abelian varieties, Ann. of Math. (2) 133(3) (1991), 549-576.

[6] M. van Frankenhuysen, The ABC conjecture implies Roth’s theorem and Mordell’s conjecture, Mat. Contemp. 16 (1999), 45-72.

[7] A. Granville, Some conjectures related to Fermat’s last theorem, Number Theory, R. A. Mollin, ed., Walter de Gruyter, Berlin, New York, 1990, pp. 177-192.

[8] A. Granville and H. M. Stark, abc implies no Siegel zeros for L-functions of characters with negative discriminant, Invent. Math. 139 (2000), 509-523.

[9] M. Hall, The Diophantine equation Computers in Number Theory, A. Atkin and B. Birch, eds., Academic Press, 1971.

[10] M. Hindy and J. H. Silverman, Diophantine Geometry, an Introduction, Springer, New York, 2000.

[11] J. P. Jones, D. Sato, H. Wada and D. Wiens, Diophantine representation of the set of prime numbers, Amer. Math. Monthly 83 (1976), 449-464.

[12] D. W. Masser, Open problems, Proc. Symp. Analytic Number Theory, W. W. L. Chen, ed., Imperial College, London, 1985.

[13] Y. Matiyasevich, The Diophantiness of enumerable sets, Dokl. Akad. Nauk SSSR 191 (1970), 279-282 (in Russian).

[14] P. Mihăilescu, Primary cyclotomic units and a proof of Catalan’s conjecture, J. Reine Angew. Math. 572 (2004), 167-195.

[15] R. A. Mollin and P. G. Walsh, A note on powerful numbers, quadratic fields and the Pellian, C. R. Math. Rep. Acad. Sci. Canada 8(2) (1986), 109-114.

[16] P. Vojta, Diophantine approximation and value distribution theory, Lecture Notes in Math. 1239, Springer, Berlin, 1987.

Keywords and phrases: ABC-conjecture, Diophantine analysis, Fermat equation, Catalan equation.

 


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