Elementary Number Theory - 7 Edition - Chapter 3 - Problem 5
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# (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

Problem 5

(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)?

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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

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