A claimed constructive proof that, for each of the four rational 2-torsion structures, infinitely many good Frey curves exist.
Barrios, Caleb Tillman, and Charles Watts, Exceptional abc triples for frey curves with torsion subgroups z_ 2 z_ 4 and z_ 2 z_ 8 , MSRI Journal (2010)
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A Constructive Proof of Masser's Theorem
A claimed constructive proof that, for each of the four rational 2-torsion structures, infinitely many good Frey curves exist.