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MATH 2601 - FoMP - Homework 2
Problem 1. Let c be a common divisor of positive integers a and b. Let g = GCD(a, b). Show that c|g. Hint. Use the property that g can be written as an integer combination of a and b.
Problem 2. Here is another way to prove that there are infinitely many primes. Suppose there are only finitely many, and that p1, p2, . . . , pk are all of them. Then consider the integer M = Qk i=1 pi p1 + Qk i=1 pi p2 + · · · + Qk i=1 pi pk .
Complete the proof.
Problem 3. Find integer solutions to the equation 990x + 84y = 24, using the (extended) GCD algorithm.
Additionally, turn in the following problems from Hammack’s book. 1.4: 6, 18 1.8: 4, 8, 14 2.5: 10 2.6: 6, 10
Optional Problems (No need to submit). 1.1: 52 1.3: 2, 10, 14 1.4: 14, 16, 20 2.3: 2, 6, 10, 12 2.6: 12, 14