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Theorem 1. For every prime p, /p is irrational. Proof. Write your proof here... Theorem 2. Let a, b, c E Z such that gcd(a, c) = gcd(b, c) = 1. Then gcd(ab, c) = 1. Proof. Write your proof here... Theorem 3. Let p E Z with p > 1. Suppose every integer n, with 2 < n < VP, does not divide p. Then is prime. Proof. Write your proof here...

Theorem 1. For every prime p, /p is irrational. Proof. Write your proof here... Theorem 2. Let a, b, c E Z such that gcd(a, c) = gcd(b, c) = 1. Then gcd(ab, c) = 1. Proof. Write your proof here... Theorem 3. Let p E Z with p > 1. Suppose every integer n, with 2 < n < VP, does not divide p. Then is prime. Proof. Write your proof here...

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help me with problem 1 on how to prove the 3 things asked in it. Your help would mean a lot to me! :) I have uploaded a picture for this question: 

Problems Problem 1. For this first problem, give a proof of each mathematical statement below. You can use any proof technique we have discussed in the class. Each proof will be graded as one på problem (i.e. with either a passing mark or a not passing mark). Theorem 1. For every prime p, Vp is irrational. Proof. Write your proof here... Theorem 2. Let a, b, c E Z such that gcd(a, c) = gcd(b, c) = 1. Then gcd(ab, c) = 1. Proof. Write your proof here... Theorem 3. Let p e Z with p > 1. Suppose every integer n, with 2 < n < Vp, does not divide p. Then p is prime. Proof. Write your proof here...
Transcribed Image Text:Problems Problem 1. For this first problem, give a proof of each mathematical statement below. You can use any proof technique we have discussed in the class. Each proof will be graded as one på problem (i.e. with either a passing mark or a not passing mark). Theorem 1. For every prime p, Vp is irrational. Proof. Write your proof here... Theorem 2. Let a, b, c E Z such that gcd(a, c) = gcd(b, c) = 1. Then gcd(ab, c) = 1. Proof. Write your proof here... Theorem 3. Let p e Z with p > 1. Suppose every integer n, with 2 < n < Vp, does not divide p. Then p is prime. Proof. Write your proof here...
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