Problem 2 Show All Work 10 Points Each Below Is Given A Proof Of A Result What Result Is Proved Explain Clearly And 1 (49.22 KiB) Viewed 37 times
Problem 2 Show All Work 10 Points Each Below Is Given A Proof Of A Result What Result Is Proved Explain Clearly And 2 (56.19 KiB) Viewed 37 times
Problem 2 Show All Work 10 Points Each Below Is Given A Proof Of A Result What Result Is Proved Explain Clearly And 3 (56.19 KiB) Viewed 37 times
Problem 2 Show all work. (10 points each) Below is given a proof of a result. What result is proved? Explain clearly and state the result. Next, proceed to construct your own proof with your own personal style. Proof Let a 2 (mod 4) and b = 1 (mod 4) and assume, to the contrary, that 4 (a²+2b). Since a = 2 (mod 4) and b = 1 (mod 4), it follows that a = 4r + 2 and b = 4s + 1, where r, s E Z. Therefore, a²+2b = (4r + 2)2 +2 (4s + 1) = (16r² +16r+4) + (8s+2) = 167² +16r+8s +6. Since 4 (a²+2b), we have a² + 2b = 4t, where t € Z. So, 16r² + 16r+8s + 6 = 4t and 6 = 4t 16r² - 16r-8s = 4 (t-4r²-4r - 2s). Since t-47²-4r - 2s is an integer, 416, which is a contradiction. ■
Problem 2 Show all work. (10 points each) Below is given a proof of a result. What result is proved? Explain clearly and state the result. Next, proceed to construct your own proof with your own personal style. Proof Let a = 2 (mod 4) and b= 1 (mod 4) and assume, to the contrary, that 4 (a² + 2b). Since a = 2 (mod 4) and b = 1 (mod 4), it follows that a = 4r + 2 and b= 4s + 1, where r, s E Z. Therefore, a² + 2b = (4r + 2)² +2 (4s + 1) = (16r² + 16r+4) + (8s+2) 167² +16r+8s +6. Since 4 (a²+2b), we have a² + 2b = 4t, where t & Z. So, 167² +16r+8s + 6 = 4t and 6 = 4t 16r²16r - 8s=4 (t-4r² - 4r - 2s). Since t 42-4r - 2s is an integer, 416, which is a contradiction. ■
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