A Note on the Exponential Diophantine Equation x2+q2m=2yp

Jian Ping Wang

doi:10.4028/www.scientific.net/AMM.241-244.2650

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 241-244A Note on the Exponential Diophantine Equation...

A Note on the Exponential Diophantine Equation x²+q^2m=2y^p

Abstract:

ln this paper, using a deep result on the existence of primitive divisors of Lehmer numbers given by Y. Bilu, G. Hanrot and P. M. Voutier, we prove that the equation has no positive integer solution (x, y, m, p, q), where p and q are odd primes with p>3, gcd(x, y)=1 and y is not the sum of two consecutive squares.

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Periodical:

Applied Mechanics and Materials (Volumes 241-244)

Pages:

2650-2653

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.241-244.2650

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Online since:

December 2012

Authors:

Jian Ping Wang

Keywords:

Existence, Exponential Diophantine Equation, Primitive Divisor of Lehmer Number

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References

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