On the Diophantine equation X~2(2~(2m) + 1)Y~4

摘要

Using a recent result of Akhtari on quartic Thue equations, it is shownthat the quartic equation X~2 — (2~(2m)+ 1)Y~4= —2~(2m)has at most 12 solutions in oddpositive integers X , Y > 1.