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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, 4 months ago

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Hint Staff · 4 years, 4 months ago

I think there will be infinitely many solution of the form x=2y......... · 4 years, 4 months ago

It means that (x-2y) is a factor of the given equation. · 4 years, 4 months ago

But you need to show all of them. (2a,a), where a is a natural number, is one possibility. Think of others. · 4 years, 4 months ago

are 1 and 0 the only solution? · 4 years, 4 months ago

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. · 4 years, 4 months ago

1 is a sol.......and also -1 i guess · 4 years, 4 months ago

Well 1 is a possibility, but not -1, because -1 is a negative integer!! · 4 years, 4 months ago