High School Mathematics Extensions/Further Modular Arithmetic/Problem Set

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 xy 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 h2g, then g is a generator mod p. That is gq ≠ 1 for all q < p - 1.