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Show by direct proof,If n is odd, then (n^2− 1) is a multiple of 8. |
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Answer» Answer: >> N = 2m + 1 >> n + 1 = 2m + 2 >> n − 1 = 2m >> n^2 − 1 = (n+1) * (n−1) = (2m + 2) * (2m) = 4m * (m+1) >> at least one of m,m+1 is EVEN thus, >> m * ( m + 1 ) = 2k then >> n^2 − 1 = 4 (2k) = 8k ⟹ 8 ∣ n^2 − 1 ************** ~ i hope i was able to help you. ~~ If u like it plz mark it brainiest ~~~ Have a great DAY ahead! |
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