Chabauty methods and covering techniques applied to generalized Fermat equations

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HANDBOOK OF MAGMA FUNCTIONS (2011, methodology): “A sieve method, described in Appendix A of [Bru02], is used.”
Chabauty for symmetric powers of curves (2009, methodology): “(b) The second is that the Chabauty–Coleman strategy can often be adapted to compute C(K), as in [3], [4], [20], [22], [23], [36], [57].”
Explicit Chabauty over number fields (2010, methodology): “urves of the form y2 = x5 + A [57], and the number of rational points on twists of a given curve [56]. (b) The second is that the Chabauty–Coleman strategy can often be adapted to compute C(K), as in [6], [7], [32], [34], [35], [42], [59], and even the K-rational points on the symmetric powers of C ”
Torsion points on families of simple abelian surfaces and Pell's equation over polynomial rings (with an appendix by E. V. Flynn) (2015, background): “Writing this period as an integral linear combination of f̃(tn), g̃(tn), k̃(tn), l̃(tn) we see easily that the coefficients are O(1).”
Integral points on hyperelliptic curves (2008, unknown): “N T ] 1 6 M ar 2 01 Y 2 ) = ( X 5 ) .”