Exercise 2.4.7. Let n be an integer. Using only the fact that every integer is even or odd, and without using Corollary 5.2.5, prove that precisely one of the following holds: either n = 4k for some integer k, or n = 4k+ 1 for some integer k, or n = 4k+2 for some integer k, or n = 4k+3 for some integer k.

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