Prove that if n is an odd integer, there is an integer in such that n = 8m + 1 or n = 8m + 3 or n = 8m + 5 or n = 8m + 7. (You may use the result of Exercise.)
[BB] Prove that if n is an odd integer then there is an integer n such that n = 4m + 1 or n = 4m + 3.
[Hint: Consider a proof by cases.]
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