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:
so far i have completed the square to get the following:
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You have a difference of squares. What differences of squares can give you 17?
would (y+x+1)(y-x-1) = 17
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
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