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M27-02: If x and y are integers, is y an even integer?

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If x and y are integers, is y an even integer?

(1) 4y^2+3x^2=x^4+y^4

(2) y=4x^2

The official answer is A, and the logic is clear to me.

But, is it possible in the first equations also to have x = y = o? Shouldn't the answer be E in such case?
It is not explicitly stated in the wording that x and y are different non-zero integers?

Most probably I just missed smth, so would be grateful for your explanations
Thanks in advance!

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