Show that n^2-1 is divisible by 8 ,if n is an odd positive integer
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Step-by-step explanation:
If n is an odd number, then n = 4x + 1, for any number x.
n^2 - 1
= (4x + 1)^2 - 1
= 16x^2 + 1 + 8x - 1
= 16x^2 + 8x
= 8(2x^2 + x)
Clearly we can see that 8(2x^2 + x) is divisible by 8.
Hence proved that n^2-1 is divisible by 8 ,if n is an odd positive number.
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