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Hey everyone ❤❤❤If n is ab odd integers , then show that n^2-1 is divisible by 8.please send answer fast ita urgent. |
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Answer» _______________________________ Step-by-step explanation: Any odd integers in the form 4m + 1 or 4m + 3 for some integer m. When n = 4m+1 => n²-1 = (4m+1)²-1 => n²-1 = 16m² + 8M +1-1 => n²-1 = 8m ( 2m+1). => n²-1 is divisible by 8 When n= 4m+3 => n²-1 = (4m+3)²-1 => n²-1 = 16m² + 24m +9-1 => n²-1 = 8 ( 2m²+3m+1) => n²-1 is divisible by 8 Hence, n²-1 is divisible by 8 if n is odd POSITIVE integer. |
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