Homework 5
Due: Friday, September 23

  1. Let $\varphi(N)$ denote the Euler totient function. Suppose you know that $\varphi(N) = 1000$. Find a small number $b$ (say, three or fewer digits) which satisfies $7^{3003} \equiv b \bmod N$.

  2. Suppose $p$ and $q$ are distinct primes.
    \begin{alphabetize} \item How many numbers between $1$\ and $pq$\ are divisible ... ...e divisible by both $p$ and $q$? \item What is $\varphi(pq)$? \end{alphabetize}
    You should argue directly, without reference to material from class from the week of September 19.

  3. [TW] 3.13.20abc.
  4. [TW] 3.13.20de.

  5. [TW] 3.13.15.


Jeff Achter