# Ordered Pairs Question

• September 20th 2010, 06:54 PM
hsidhu
Ordered Pairs Question
Hi, I've started solving this problem, but I don't know how to finish it off.

Find all ordered pairs of integers (x,y) such that: $x^2 + 2x + 18 = y^2$

so far i have completed the square to get the following:

$y^2 - (x+1)^2 = 17$

Thanks!
• September 20th 2010, 07:27 PM
Prove It
You have a difference of squares. What differences of squares can give you 17?
• September 20th 2010, 08:27 PM
hsidhu
would (y+x+1)(y-x-1) = 17
work?
• September 20th 2010, 10:31 PM
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Quote:

Originally Posted by hsidhu
would (y+x+1)(y-x-1) = 17
work?

Yes, you have transformed the problem into one of integer factorization, which is rather easy here since 17 is prime.

Four candidate solutions:

y+x+1 = 1 AND y-x-1 = 17
y+x+1 = 17 AND y-x-1 = 1
y+x+1 = -1 AND y-x-1 = -17
y+x+1 = -17 AND y-x-1 = -1