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Non-negative Integral solutions

I have a nice question for you all: Find all Non-negative integral solutions to the following equation:

\(4x^4+12x^3y+4x^3-7x^2y^2+4x^2y-25x^2-48xy^3-15xy^2-25x-36y^4-18y^3+100y^2+50y=0\)

Note by Shourya Pandey
4 years, 9 months ago

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Hint

Calvin Lin Staff - 4 years, 9 months ago

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I think there will be infinitely many solution of the form x=2y.........

Kiran Patel - 4 years, 9 months ago

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It means that (x-2y) is a factor of the given equation.

Shourya Pandey - 4 years, 9 months ago

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But you need to show all of them. (2a,a), where a is a natural number, is one possibility. Think of others.

Shourya Pandey - 4 years, 9 months ago

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are 1 and 0 the only solution?

Ekdeep SIngh Lubana - 4 years, 9 months ago

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Everyone should try this question.....you may take y=kx and see that for which value of k is the lhs always zero. Then y-kx becomes a factor of the lhs.

Shourya Pandey - 4 years, 9 months ago

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1 is a sol.......and also -1 i guess

Superman Son - 4 years, 9 months ago

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Well 1 is a possibility, but not -1, because -1 is a negative integer!!

Shourya Pandey - 4 years, 9 months ago

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yeah

Superman Son - 4 years, 9 months ago

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