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KMO 1997 Problem 6

    Find all polynomial P(x,y)P(x,y) for any reals x,yx,y such that (i) x100+y100≤P(x,y)≤101(x100+y100)x^{100}+y^{100}\le P(x,y)\le 101(x^{100}+y^{100}) (ii) (x−y)P(x,y)=(x−1)P(x,1)+(1−y)P(1,y).(x-y)P(x,y)=(x-1)P(x,1)+(1-y)P(1,y).

    Dataset text AI-MO AoPS. Quoted with source.

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