In this repository, we include all the code necessary for the computations in the paper. If you detect any bugs, or have any questions or comments, feel free to contact me in [email protected]
Note that this code uses existing code from other papers, namely the following:
(1) A. Gherga and S. Siksek, "Efficient resolution of Thue-Mahler equations",
https://arxiv.org/abs/2207.14492. The code is in Gherga's GitHub repository:
https://github.com/adelagherga/ThueMahler/tree/master/Code/TMSolver.
(2) M. Mignotte and P. Voutier, "A kit on linear forms in three logarithms",
https://arxiv.org/abs/2205.08899. The code is in Voutier's GitHub repository:
https://github.com/PV-314/lfl3-kit.
We briefly detail all existing folders and their contents.
-> MAGMA: This involves all computations for most of the papers (Sections 2-7).
-> exponents3And4.m: This resolves the equation for n=3 and 4 by finding
S-integral point on elliptic curves (Section 2).
-> yOdd.m: This code adapts the computational methodology in Section 3,
including the use of Lehmer sequences and the computational
improvements to avoid solving Thue-Mahler equations.
IMPORTANT: It is necessary to include (1) for this to work.
-> thueMahler.m: This includes the resolution of Thue-Mahler equation in
Section 4. In order for this to work, n should be relatively
small (n < 17).
IMPORTANT: It is necessary to include (1) for this to work.
-> boundExponent.m: This includes all the techniques that we develop in Section
6 in order to bound the exponent p.
-> specificExponents.m: This includes all the techniques that we present in
Section 7 in order to show that there are no exponents for
a fixed value of p.
-> PARI-GP: This includes the computations on linear forms in logarithms in Section 8. We note that this code is an adaptation of (2), and it is required to work in conjunction with it. Numbers should be modified inside the code in order for this to work.
-> lfl.gp: Module including the functions and quantities relevant to our problem.