mazon.com - Onli... ... LastPass password... Express VPN U Utomik Games Homework-M4T3 Primes Math 1166 Discrete Mathematics 1. [4 points] Is the following True or False: Vm E Z+, is 6m x (2m + 10) divisible by 4? If True, provide a proof. If False, provide a counterexample. 2. [12 points] Let a, b, de N. (a) Show that (provide a proof): if d | a and d | b, then d | b + a. b) Show that (provide a proof) if d | a and d | b, then d | b - a. (c) Assume b > a, show that (provide a proof) ged(a, b) | b - a. 3. [2 points] When is the following True: lem(a, b) = ab? Explain your answer. 4. [6 points] (a) What is the prime factorization of 2800 and 6125? (b) Compute ged(2800, 6125) using the prime factorization of both numbers. (c) Compute lem (2800, 6125) using the prime factorization of both numbers. 5. [6 points] Let p be a prime number and a, be N. Consider the True 'if . .. then' statement, called Euclid's Lemma: If p | ab, then p | a or p | b. () Explain the staton 8:20 PM W Rain off and on 11/15/2022 Port sc delete home end 10 F11 f12 DDI num backspace lock 7 - 00 P M home enter 4 5on.com - Onli... ... LastPass password... Express VPN TUtomik Games 2. [12 points] Let a, b, d E N. (a) Show that (provide a proof): if d | a and d | D, then d | b + a (b) Show that (provide a proof) if d | a and d | b, then d | b - a. (c) Assume b 2 a, show that (provide a proof) ged(a, b) |b - a. 3. [2 points] When is the following True: lem(a. b) - ab? Explain your answer. 4. [6 points] (a) What is the prime factorization of 2800 and 6125? (b) Compute ged(2800, 6125) using the prime factorization of both numbers. (c) Compute lem (2800, 6125) using the prime factorization of both numbers. 5. [6 points] Let p be a prime number and a, be N. Consider the True 'if . .. then statement, called Euclid's Lemma: If p | ab, then p | a or p | b. (a) Explain the statement using an example. b) Write the converse of the statement. Is the converse True or False? Explain. (c) Write the contrapositive of the statement. Is the contrapositive True or False? Explain. 8:20 PM W Rain off and on A 11/15/2022 home end 09 UP 112 "port sc delete num backspace lock 7 - 00 P L M home