  Given a linear equation L, a set A of integers is L-free if A does not
contain any non-trivial solutions to L. Meeks and Treglown showed that for
certain kinds of linear equations, it is NP-complete to decide if a given set
of integers contains a solution-free subset of a given size. Also, for
equations involving three variables, they showed that the problem of
determining the size of the largest solution-free subset is APX-hard, and that
for two such equations (representing sum-free and progression-free sets), the
problem of deciding if there is a solution-free subset with at least a
specified proportion of the elements is also NP-complete.
  We answer a number of questions posed by Meeks and Treglown, by extending the
results above to all linear equations, and showing that the problems remain
hard for sets of integers whose elements are polynomially bounded in the size
of the set. For most of these results, the integers can all be positive as long
as the coefficients do not all have the same sign.
  We also consider the problem of counting the number of solution-free subsets
of a given set, and show that this problem is #P-complete for any linear
equation in at least three variables.
