Question

Show that n2 - 1 is divisible by 8, if n is an odd positive integer.
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Answer 1

ANSWER

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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Answer 2

Answer:

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Show that n2−1 is divisible by 8, if n is an odd positive integer. Any odd positive number is in the form of (4p+1)or(4p+3) for some integer P. Therefore, n2−1 is divisible by 8 if n is an odd positive integer.

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