If n eN and n > 4 then show that in > n2
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Answer:
any odd opposite number is in the form of
(4p+1) or (4p+3) some integers P
let
n=4p+3
n²-1=(4p+1)²-1=16p²+8p+1-1=
==>n²-1 is divisible by 8
n²-1=(4p+3)²-1=16p²+8p+9-1=
8(2p²+3p+1)
==>n²-1 is divisible by 8
there fore,n²-1 is divisible by 8if n is an odd opposite integers
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