High School Mathematics Extensions/Further Modular Arithmetic/Problem Set

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.