Solve the Diophantine equation $a^2(2^a-a^3)+1=7^b$.
The OP claims to have solved this some time ago (see comment under main question). I'm just adding this answer so that this thread doesn't show up in a "No Answers" search/filter.
The OP claims to have solved this some time ago (see comment under main question). I'm just adding this answer so that this thread doesn't show up in a "No Answers" search/filter.