Given the following equation: $$ x^{2} - y^{2}=17, \quad 0\neq x,y\in \mathbb N$$
I know for example that one solution is $x=9$, $y=8$, but I do not know how to get it.
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2Hint: Can you factorise $x^2-y^2$? – Mark Bennet Nov 17 '14 at 13:29
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As long as I get appropriate solution for the equation. – Jimmy_J Nov 17 '14 at 13:35
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rewrite your equation in the form $(x-y)(x+y)=1\cdot 17$ from here you will get $x-y=1$ and $x+y=17$ the other case is impossible. or we have $(x-y)(x+y)=(-1)\cdot (-17)$
Dr. Sonnhard Graubner
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@Dr. Sonnhard Graubner: In that case I get a single solution. That means no more solutions in N ? – Jimmy_J Nov 17 '14 at 13:52