Math Olympiad Challenge - Diophantine Equation

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Math Olympiad Challenge - Diophantine Equation
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Me simply thinking about 1/4008 + 1/4008 = 1/2004

mannatrana
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I did not know how easy it was to find the total factors of a factorable number. I wonder how that is derived. Very smart like always.

MrGnome-ngjv
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By observation, x=y=4008.

Thank you!😁

LawsonHanson
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and the same number of negative pair will exist

suniltshegaonkar
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What are the solutions?Please, elaborate.

DilipKumar-nskl
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x(2004 - y) + y(2004 - y) = -y²
By factoring -y² in different ways, I am clearly not getting 45 solutions.
Could you (anyone, really) tell me my mistake?

jason_schlong