The Total solution for NCERT class 6-12
(c)
At k = -1, a = 4(-1)(-1 + 1) = 0 which is divisible by 8.At k = 0, a = 4(0)(0 + 1) = 4 which is divisible by 8.At k = 1, a = 4(1)(1 + 1) = 8 which is divisible by 8.Hence, we can conclude from above two cases, if n is odd, then n2 –1 is divisible by 8.