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Two exponential Diophantine equations

Published online by Cambridge University Press:  18 May 2009

Erik Dofs
Erik Dofs
Affiliation:
Royal Institute of Technology, S-10044 Stockholm, Sweden
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In [3], two open problems were whether either of the diophantine equations

with n ∈ Z and f a prime number, is solvable if ω > 3 and 3 √ ω, but in this paper we allow f to be any (rational) integer and also 3 | ω. Equations of this form and more general ones can effectively be solved [5] with an advanced method based on analytical results, but the search limits are usually of enormous size. Here both equations (1) are norm equations in K (√–3): N(a + bp) = fw with p = (√–1 + –3)/2 which makes it possible to treat them arithmetically.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 2 , May 1997, pp. 231 - 232
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

REFERENCES

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