Thread: Find the ordered pairs

Hello, I'm having some trouble with the following question, and have not been able to solve it despite excessive attempts:

Find all ordered pairs of integers (x,y) such that

I tried square-rooting both sides so that the equation could be solved for y, but didn't have any luck. I also thought about using the "completing the square" method, but am not sure on how to use it in this case. I would greatly appreciate any help.

Thanks!

I found one pair. There may be others.
Look at .

Plato's suggestion, that you rewrite the equation as so that is excellent! If you let z= x+1, then that equation becomes or . Since y and z are integers, you should be able to quickly find Plato's solution as well as the three other ordered pairs satifying that equation.