With reasoning Though we are still studying aspects of logical reasoning, this i

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With reasoning

Though we are still studying aspects of logical reasoning, this is also a course in mathematical proof. Therefore, this problem is your first attempt in this course to develop a sound mathematical proof. The proof should be doable using the definitions below and elementary properties of the integers. Clearly indicate your reasoning and what properties of the integers you use. Prove that if n is an odd integer then n2 - 1 is a multiple of 8. The following definitions may be useful. An odd integer is an integer n such that n = 2k + 1 for some integer k. An integer a is a multiple of the integer b if a = bc for some integer c.

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