Question

Use mathematical induction to prove if n is a positive integer, then 8|n^2-1

Answer 1

Answer:

Step-by-step explanation:

R

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

let

n=4p+3

n  ^2 −1=(4p+1)  ^2 −1=16p  ^2 +8p+1−1=8p(2p+1)

⇒n ^2 −1 is divisible by 8

n^  2 −1=(4p+3)  ^2 −1=16p  ^2 +24p+9−1=16p^  2+24p+8 =8(2p  ^2+3p+1)

⇒n  ^2 −1 is divisible by 8

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Therefore, n  ^2 −1 is divisible by 8 if n is an odd positive integer.

hope this answer helps you .