Question

In: Advanced Math

Prove that if n is an integer and n^2 is even the n is even.

Expert Solution

Sol.- Let n is an integer and is even.

To prove:- n is even

We will prove it by using method of contradiction.

Let us assume that n is an integer and is even but n is not even.i.e. n is odd.

Since n is odd

n = 2k + 1 , for some integer k.

[on squaring both sides]

which is not possible since is even.

So, this contradicts that the fact is even.

Hence our assumption that n is not even is wrong.

Thus, if n is an integer and is even then n is also even. Hence Proved.

Colby Messinger answered 2 years ago

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