DISCRETE MATHS
posted by Don(please check my math) .
We need to show that 4 divides 1n2 whenever n is an odd positive integer.
If n is an odd positive integer then by definition
n = 2k+1 for some non negative integer, k.
Now 1  n2 = 1  (2k+1)2 = 4k24k = 4 (k24k).
k is a nonnegative integer, hence k24k is an integer. Thus by definition
of divisibility we conclude that 4 divides 1n2.
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