High School Mathematics Extensions/Further Modular Arithmetic/Problem Set
HSME |
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Further Modular Arithmetic |
Multiplicative Group and Discrete Log |
Problems & Projects |
Problem Set |
Project |
Solutions |
Exercises Solutions |
Problem Set Solutions |
Misc. |
Definition Sheet |
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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 a^{λ(m)} ≡ 1 (mod m).
3. Let p be prime such that p = 2^{s} + 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 h^{2} ≡ g, then g is a generator mod p. That is g^{q} ≠ 1 for all q < p - 1.