(1) Do the problems on separate sheets of paper (containing your name) and attac
ID: 3147189 • Letter: #
Question
(1) Do the problems on separate sheets of paper (containing your name) and attach them with a staple to this sheet. (2) Each student must work on the quiz alone. 1. Let p be a prime number. Which integers are relatively prime to p? 2. (a) Use the Euclidean Algorithm to compute the greatest common divisor of 126 and 224. (b) Express the greatest common divisor of 126 and 224 as an integer combina- tion of the two numbers. Choose ONE of the following two questions: 3. Suppose that ged(a,b) 1. (a) Does this determine ged(a2,b2)? (b) Does this determine gcd(a, 2b)? 4. Write a computer program that finds the greatest common divisor of two positive integers.Explanation / Answer
Ans 1. Any integer which is not an integral multiple of p will be relatively prime to the prime number p.
Ans 2. (a) 224 = 126*1 + 98; 126 = 98*1 + 28; 98 = 28*3 + 14; 28 = 14*2 + 0. This implies 14 is the HCF of 126 and 224.
Ans 2. (b) 14 = 2*7
Ans 3. (a) Yes, we can say that gcd(a2,b2) is 1, if gcd(a,b) = 1.
Ans 3. (b) No, we can't say about the gcd(a,2b)
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