Day 4: Modular Arithmetic & Groups

Note: today’s Replit includes solutions for the previous day’s required problems.

Lecture Topics

• notes
• remainders
• modular arithmetic
• commutative groups
  • cyclic groups

Problems

Reminders:

• You can run tests for a function by running python main.py FUNCTION_NAME from the shell.

We’ll be working in the main.py file. The hashing.py file contains solutions to yesterday’s required problems.

Some of the problems have written solutions rather than code. Put your solutions in a comment.

• required:

  • In the IntMod class:
    • __add__: gives Python’s + operator
    • __mul__: gives Python’s * operator
    • __neg__: gives Python’s unary - operator
    • __truediv__: gives Python’s / operator
    • __pow__: gives Python’s ** operator
  • order_2_element
  • WQ1: power order
  • WQ2: orders in $\mathbb{Z}_{11}^*$
  • WQ3: order patterns
  • discrete_log_7

• bonus:

  • WQ4: roots
  • my_pow