Exercise 6.2. Prove each of the following statements. (a) There exist integers a and b so that 3a - 4b = 73. (b) There exists an odd integer a and an even integer b so that 3a+4b = 17. (c) There do not exist integers a and b so that 2a + 4b = 25. (d) For every odd integer n ≥ 3 there exists an odd integer a and an even integer b so that a + b = n.

Exercise 6.2. Prove each of the following statements. (a) There exist integers a and b so that 3a - 4b = 73. (b) There exists an odd integer a and an even integer b so that 3a+4b = 17. (c) There do not exist integers a and b so that 2a + 4b = 25. (d) For every odd integer n ≥ 3 there exists an odd integer a and an even integer b so that a + b = n.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.4: Prime Factors And Greatest Common Divisor

Problem 32E: Use the second principle of Finite Induction to prove that every positive integer n can be expressed...

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