- Please Clearly Write The Proof Process Of The Question Thanks 1 (92.46 KiB) Viewed 20 times
Please clearly write the proof process of the question, thanks
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answerhappygod
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Please clearly write the proof process of the question, thanks
Please clearly write the proof process of the question,thanks
1. (15 points) Prove that (1) (5 points) Define an integer n to be great if n² – 1 is a multiple of 3. Prove that for any integer N, if N is great then N + 3 is great. (2) (5 points) Let a € Z. Prove that 3 | 8a if and only if 3 | a. (3) (5 points) Prove that if n € Z is even, then either n = 4k or n = 4k + 2 for some integer k. You may assume that every integer is either even or odd. (Food for thought: try to prove this fact.)
1. (15 points) Prove that (1) (5 points) Define an integer n to be great if n² – 1 is a multiple of 3. Prove that for any integer N, if N is great then N + 3 is great. (2) (5 points) Let a € Z. Prove that 3 | 8a if and only if 3 | a. (3) (5 points) Prove that if n € Z is even, then either n = 4k or n = 4k + 2 for some integer k. You may assume that every integer is either even or odd. (Food for thought: try to prove this fact.)
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