Proof - If the square of an integer is even,. .

[yanjt]

Hi,
I have no idea on how to start to do this question.
If the square of an integer is even,then the integer itself is even

I try to check some books but i can't get any similar examples.I wonder if I can directly prove the n=2k, n^2 = 2(2k^2).

Thanks!

 

[matt grime]

But that is the converse of what you were asked to show. You want to show that if m^2 is even, then m is even. One of the definitions of a prime number makes this instantaneous. What definitions of prime do you know?

Alternatively you can show that if n is odd, then n^2 is odd.

 

[tiny-tim]

Welcome to PF!

Hi,
I have no idea on how to start to do this question.
If the square of an integer is even,then the integer itself is even

I try to check some books but i can't get any similar examples.I wonder if I can directly prove the n=2k, n^2 = 2(2k^2).

Thanks!

Hi yanjt! Welcome to PF!

Try proving it the other way round:

if an integer is odd, its square is odd.

 

[yanjt]

Prime number is number that can be divided by or itself.
if i prove that an integer is odd,its square is odd,I am not using contradiction to prove it,right?I can show that if an integer is odd,its square is odd.Yet, how can i show that if the square of an integer is even,the integer itself is even?

Thanks for ur help!

p/s:Thanks tiny-tim!I found this website is really useful!=)

 

[matt grime]

What's wrong with using proof by contradiction?

 

[yanjt]

Nothing is wrong using contradiction.What i mean is that,i wonder if proof "if n is odd,n^2 is odd" is a kind of contradiction?