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If n is an odd integer, then show that n2 – 1 is divisible by 8.

Mathematics - Exemplar Problems

Chapter _Real Numbers


If an number is multiplied by itself,
suppose n

So, n2 - 1
= (n+1)(n-1)

Hence, both (n+1) and (n-1) are even numbers
and if (n+1) is divisible by 2, (n-1) must be divisible by 4 ( by logic)
So, n2 - 1 must be divisible by 4x2 = 8
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