The discussion revolves around finding all ordered pairs of integers (x, y) that satisfy the equation x² + 2x + 18 = y². Participants are exploring methods to approach this problem in the context of integer solutions.
The discussion is ongoing, with participants providing initial attempts and questioning the correctness of results. There is a suggestion to complete the square, and some participants are seeking confirmation on their findings.
There is a focus on integer solutions, and participants are navigating through the implications of completing the square and the resulting equations. The nature of the problem suggests constraints related to the properties of integers.
It might be helpful to complete the square. Then you would have the difference of two squares being equal to -17.spoc21 said:Homework Statement
Please find all ordered pairs of integers (x,y) such that x2 + 2x + 18 = y2
Homework Equations
x2 + 2x + 18 = y2
The Attempt at a Solution
Im not sure on how to begin. I tried square-rooting the expression, to solve for y, turning it into y = [tex]\sqrt{x + 2x + 18}[/tex]. I would greatly appreciate any help to get me started on this problem.
Thanks!