  We consider a question of finding a periodic solution for the planar
Newtonian N-body problem with equal masses, where each body is travelling along
the same closed path. We provide a computer assisted proof for the following
facts: local uniqueness and convexity of Chenciner and Montgomery Eight, an
existence (and local uniqueness) for Gerver's SuperEight for 4-bodies and a
doubly symmetric linear chain for 6-bodies.
