  A primary branch solution (PBS) is defined as a solution with $n$ independent
$m-1$ dimensional arbitrary functions for an $n$ order $m$ dimensional partial
differential equation (PDE). PBSs of arbitrary first order scalar PDEs can be
determined by using Lie symmetry group approach. Especially, one recursion
operator and some sets of infinitely many high order symmetries are also
explicitly given for arbitrary (1+1)-dimensional first order autonomous PDEs.
Because of the intrusion of the arbitrary function, various implicit special
exact solutions can be find by fixing the arbitrary functions and selecting
different seed solutions.
