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Paper   IPM / M / 8009
School of Mathematics
  Title:   On the diophantine equation x2+3=pyn
1.  Kh. Hessami Pilehrood
2.  T. Hessami Pilehrood
  Status:   Published
  Journal: Indian J. Pure Appl. Math.
  Vol.:  36
  Year:  2005
  Pages:   431-439
  Supported by:  IPM
Let p be an odd prime such that p−3 is not a perfect square. In this paper we prove that the equation x2+3=pyp−1 has no solutions in rational numbers x,y. The proof depends on the unique factorization in the ring of algebraic integers of \mathbbQ(√−3) and on certain congruence arguments. Furthermore, the equations x2+3=py[(p−1)/2] and x2+3=py6 in rationals x,y are also considered.

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