Problem

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Tags: algebra, polynomial, function, ceiling function, inequalities, algebra proposed



Determine whether there exists a polynomial f(x1,x2) with two variables, with integer coefficients, and two points A=(a1,a2) and B=(b1,b2) in the plane, satisfying the following conditions: (i) A is an integer point (i.e a1 and a2 are integers); (ii) |a1b1|+|a2b2|=2010; (iii) f(n1,n2)>f(a1,a2) for all integer points (n1,n2) in the plane other than A; (iv) f(x1,x2)>f(b1,b2) for all integer points (x1,x2) in the plane other than B. Massimo Gobbino, Italy