Modular Arithmetic: Addition in Motion

Topics Covered (14 minutes 47 seconds):

  • Examples of additive dynamical portraits
  • Proof that f(x) = x+a is bijective, which proves the pictures contain only cycles
  • Proof that the cycles are all the same size
  • Process of exploration and conjecture for the cycle size/number
  • A full description of the dynamical portrait with proof

Background needed:

  • the definitions of function, injectivity, surjectivity, bijectivity
  • the ability to use modular arithmetic in practice (see Modular Arithmetic: User’s Manual.)
  • the video Modular Arithmetic:  In Motion, which introduces dynamical portraits and proves basic properties:
    • the portrait consists of cycles if and only if the associated function is a bijection

Materials and links: