Question

Prove that any even positive integer is of the form 4k or 4k+2, where k is an integer.

Answer 1

Answer:

Any natural number is either even or odd.

So any natural number can be represented as 2n or 2n+1 where n∈N.

Now, (2n)2=4n2 which is of the form 4k where k∈N

AND

(2n+1)2=4n2+4n+1=4n(n+1)+1 which is of the form 4k+1 where k∈N.

Hope this helps.