Question

if n is a positive odd integer then show that n square - 1 is divisible by 8

Answer 1

hii Shanin3 !!
Here's ur solution to dat....

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Given, 'n' is a positive odd integer.

therefore, n can be expressed in 4q+1 , q belongs to Z (integer)

therefore, n = 4q +1
n^2 - 1 = (4q+1 )^2 - 1
= (4q) ^2 + 2 . 4q. 1 + (1)^2 - 1
= 16q^2 + 8q + 1 - 1
= 8 (2q +q)

Therefore, n^2 -1 is divisible by 8.

Hope it helps ya ☺✌