Find all three digit even numbers N such that 693 times N is a perfect square.
I have no idea how to go about this?
Please help urgently!
First of all observe that . So if is a perfect square, then since only one factor of 7 and 11. More clearly .
Now choose even k such that is a three digit number
You will see that for k= 4, N is already a four digit number. Thus k=2 is the only answer.
Or
So the only three digit that satisfies is