Question

show that every positive integer is either even or odd

Answer 1

Let I be a positive integer.
We can now write I in the form of 
I = pq + r
So, pq + r can either be even or odd, since x+y yields either even or odd no
=》if pq + r is even
pq + r = 2x
And if odd 
pq + r = 2x + 1
So,
I = 2x or 2x + 1
=》 I = odd or even

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