## Solution for problem 5 Chapter 3

# (a) Given that p is a prime and p I an, prove that pn I an.(b) If gcd(a, b) = p, a

Elementary Number Theory | 7th Edition

(a) Given that p is a prime and p I an, prove that pn I an.(b) If gcd(a, b) = p, a prime, what are the possible values of gcd(a2, b2), gcd(a2, b) andgcd(a3, b2)?

**Accepted Solution**

**Step 1 of 3**

INTRODUCTORY STATISTICS CH 5 5.1 Randomness: no purpose or aim STATISTICAL RANDOMNESS: -no predictable pattern -no values are shown more than another one -HARD TO ACHIEVE WITHOUT TECHNOLOGY Psuedo random numbers: computer generate random numbers that are generated by a seed value that starts at a randomsequence Streak: a repeated value of data next to each other -ex: when flipping heads or tails & getting heads twice in a row “streak of two heads” -long streaks make randomness/chance look like a pattern but they aren’t Probability: used to determine how often randomness occurs -theoretical probability: relies on theory. Long run relative frequencies that happens an infinite amount of repetitions -empirical p

###### Chapter 3, Problem 5 is Solved

**Step 2 of 3**

**Step 3 of 3**

Enter your email below to unlock your **verified solution** to:

(a) Given that p is a prime and p I an, prove that pn I an.(b) If gcd(a, b) = p, a