SOLUTION: Prove that there are natural numbers x, y such that x^3 + 4 = 17y^2 and xy = 8. How many examples are there?

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Question 1033733: Prove that there are natural numbers x, y such that
x^3 + 4 = 17y^2 and xy = 8. How many examples are there?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
If x and y are supposed to be natural numbers such that xy = 8, then the only ordered pairs (x,y) possible are (1,8), (2,4), (4,2), and (8,1).
By direct substitution, (1,8), (2,4), and (8,1) will not satisfy x%5E3+%2B+4+=+17y%5E2. (Use you calculator to confirm!) The only pair that satisfies is (4,2).