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ON THE EXPONENTIAL DIOPHANTINE EQUATION x2+p2m=2yn

  • HUILIN ZHU (a1), MAOHUA LE (a2) and ALAIN TOGBÉ (a3)
Abstract

Let p be an odd prime. In this paper, we consider the equation and we describe all its solutions. Moreover, we prove that this equation has no solution (x,y,m,n) when n>3 is an odd prime and y is not the sum of two consecutive squares. This extends the work of Tengely [On the diophantine equation x2+q2m=2yp, Acta Arith.127(1) (2007), 71–86].

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Copyright
Corresponding author
For correspondence; e-mail: hlzhu@xmu.edu.cn
Footnotes
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The first author was partly supported by the Fundamental Research Funds for the Central Universities (No. 2011121039). The second author was supported by the National Science Foundation of China (No. 10971184). The third author was supported by Purdue University North Central.

Footnotes
References
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[1]Abu Muriefah, F. S., Luca, F., Siksek, S. and Tengely, S., ‘On the diophantine equation x 2+C=2y n’, Int. J. Number Theory 5(6) (2009), 11171128.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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