In this note we solve the twisted conjugacy problem for braid groups, i.e. we
propose an algorithm which, given two braids u,v∈Bn and an automorphism
ϕ∈Aut(Bn), decides whether v=(ϕ(x))−1ux for some x∈Bn. As a corollary, we deduce that each group of the form Bn⋊H, a
semidirect product of the braid group Bn by a torsion-free hyperbolic group
H, has solvable conjugacy problem