If n is an odd integer , then show that n^2-1 is divisible by 8
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An odd integer n is either a 4k+1 or a 4k+3.
(4k+1)2 – 1 = 16k2+ 8k + 1 - 1 =8(2k2 +k), which is a multiple of 8.
(4k+3)2 – 1 = 16k2+ 24k + 9 - 1 =8(2k2 +3k + 1), which is a multiple of 8.
(4k+1)2 – 1 = 16k2+ 8k + 1 - 1 =8(2k2 +k), which is a multiple of 8.
(4k+3)2 – 1 = 16k2+ 24k + 9 - 1 =8(2k2 +3k + 1), which is a multiple of 8.
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