High School Mathematics Extensions/Further Modular Arithmetic/Problem Set
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| HSME |
| Content |
|---|
 Further Modular Arithmetic |
| Multiplicative Group and Discrete Log |
| Problems & Projects |
| Problem Set |
| Project |
| Solutions |
| Exercises Solutions |
 Problem Set Solutions |
| Misc. |
| Definition Sheet |
| Full Version |
| PDF Version |
1. Suppose in mod m arithmetic we know x ≠ y and
find at least 2 divisors of m.
2. Derive the formula for the Carmichael function, λ(m) = smallest number such that aλ(m) ≡ 1 (mod m).
3. Let p be prime such that p = 2s + 1 for some positive integer s. Show that if g is not a square in mod p, i.e. there's no h such that h2 ≡ g, then g is a generator mod p. That is gq ≠ 1 for all q < p - 1.
