IMO Shortlist 1985 problem 12


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2. travnja 2012.
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A sequence of polynomials P_m(x, y, z), m = 0, 1, 2, \cdots, in x, y, and z is defined by P_0(x, y, z) = 1 and by
P_m(x, y, z) = (x + z)(y + z)P_{m-1}(x, y, z + 1) - z^2P_{m-1}(x, y, z)
for m > 0. Prove that each P_m(x, y, z) is symmetric, in other words, is unaltered by any permutation of x, y, z.
Izvor: Međunarodna matematička olimpijada, shortlist 1985