if n is a odd positive integer, show that(n²-1) is divisible by 8​

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if n is a odd positive integer, show that(n²-1) is divisible by 8​

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Amelia 1 month 2021-08-12T19:46:54+00:00 1 Answer 0 views 0

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    2021-08-12T19:47:57+00:00

    Step-by-step explanation:

    Any odd positive number is in the form of (4p+1)or(4p+3) for some integer P.

    letn=4p+3n2−1=(4p+1)2−1=16p2+8p+1−1=8p(2p+1)⇒n2−1isdivisibleby8n2−1=(4p+3)2−1=16p2+24p+9−1=16p2+24p+8=8(2p2+3p+1)⇒n2−1isdivisibleby8

    Therefore, n2−1 is divisible by 8 if n is an odd positive integer.

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