Due Friday, September 2nd

For Friday:

  1. Write me a paragraph “check-in”; how do you feel the class is going?  What are challenges, what can I do to help with those?
  2. Compare your last daily post solutions with my solutions.  Make sure you understand your errors or incomplete questions (if any).  Ask me if you have questions, I’m easy to find on discord.
  3. Use Euler’s And Fermat’s Little theorems (and maybe successive squaring or double-and-add/square-and-multiply) to compute $59^{(7^{115})} \pmod{26}$ by hand.
  4. Use Euler’s Theorem to prove the following:  Let $a \in (\mathbb{Z}/n\mathbb{Z})^*$ have multiplicative order $k$.  Then $k$ divides $\varphi(n)$ (the Euler phi function of $n$).  I will provide some hints on discord using the ‘spoiler’ feature.