Suppose n is an integer. Prove that the following three statements are equivalent i. n² is even ii. n + 3 is odd iii. 5n + 2 is even by proving (i) ? (ii) and (ii) ? (iii).
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Let \( n = 2k \) for some integer \( k \). Then \( n + 3 = 2k + 3 \), which is odd. - **(ii) ⇒ (i):** If \( n + 3 \) is odd, then \( n \) must be even (since adding 3 to an even number results in an odd number). Let \( n = 2k \) for some integer Show more…
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