3. Suppose that p and q are odd primes. Show that pq is a pseudoprime base 2 if and only if ord, (2)| (q-1) and ord, (2) | (p-1). Here, if gcd(a, p) = 1, we use the notation ord,(a) for the order of the element [a], in the group Up.
3. Suppose that p and q are odd primes. Show that pq is a pseudoprime base 2 if and only if ord, (2)| (q-1) and ord, (2) | (p-1). Here, if gcd(a, p) = 1, we use the notation ord,(a) for the order of the element [a], in the group Up.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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[Number Theory] How do you solve question 3? The second picture is for definitions. thanks
Additional information:
- We say that a group G is abelian if its elements commute, that is, gh = hg for all g, h in G
- Un is an abelian group under multiplication mod (n)
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