Solution:Any odd integer n is of the form 4m + 1 or 4m + 3.
=> n2 – 1 = (4m + 1)2 – 1= 16m2 + 8m= 8(2m2 + m),which is divisible by 8.Also, n2 – 1 = (4m + 3)2 – 1= 16m2 + 24m + 8= 8(2m2 + 3m + 1),which is divisible by 8.Hence, n2 – 1 is divisible by 8 for any odd integer n.
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