Show that n2 1 is divisible by 8
Asked by admin @ in Math viewed by 320 People
If n is an odd integer then prove that n2 -1 is divisible by 8
Answered by admin @
We know ,
odd number in the form of (2P +1) where P is a natural number ,
so, n² -1 = (2P + 1)² -1
= 4P² + 4P + 1 -1
= 4P² + 4P
now , checking :
P = 1 then,
4P² + 4P = 4(1)² + 4(1) = 4 + 4 = 8 , it is divisible by 8.
P =2 then,
4P² + 4P = 4(2)² + 4(2) =16 + 8 = 24, it is also divisible by 8 .
P =3 then,
4P² + 4P = 4(3)² + 4(3) = 36 + 12 = 48 , divisible by 8
hence, we conclude that 4P² + 4P is divisible by 8 for all natural number .
hence, n² -1 is divisible by 8 for all odd value of n .
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