On the Diophantine equation yⁿ = f(x)ⁿ + g(x)

R. Srikanth and S. Subburam
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 17, 2011, Number 3, Pages 18–21
Full paper (PDF, 131 Kb)

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Authors and affiliations

R. Srikanth
Department of Mathematics, Sastra University
Thanjavur-613 401, India

S. Subburam
Department of Mathematics, Sastra University
Thanjavur-613 401, India

Abstract

In this paper, we simplify the algorithm of Szalay [5].

Keywords

• Diophantine equation
• Irreducible polynomial
• Height
• Monic polynomial

AMS Classification

• 11B41

References

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3. Runge, C. Uber ganzzahlige Losungen von Gleichungen zwischen wei Veranderlichen. J. reine Angew. Math. 100 (1887) 425–435.
4. Szalay, L. Fast Algorithm for Solving Superelliptic Equations of Certain types. Acta Acad. Paed. Agriensis, Sectio Mathematicae, 27 (2000) 19–24.
5. Szalay, L. Superelliptic equation y ^p = x ^{k p} + a_kp-1x^kp-1 + …+ a₀ . Bull. Greek Math. Soc.,
   46 (2002) 23–33.