High School Mathematics Extensions/Further Modular Arithmetic/Problem Set
|Further Modular Arithmetic|
|Multiplicative Group and Discrete Log|
|Problems & Projects|
|Problem Set Solutions|
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.