Rational Relativistic Collisions
  If two point particles collide relativistically in one dimension, and the masses, velocities and gamma factors of the incoming particles are rational numbers, then the velocities and gamma factors of the outgoing particles are rational. Numerous examples can be found using Pythagorean triples. At all velocities, the collision results in a Lorentzian reflection of the 2-momenta of the particles. 
N.S. Manton
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