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USAMO
1982


Problem - 3496
Let Xr=xr+yr+zr with x,y,z real. It is known that if S1=0, () Sm+nm+n=SmmSnn for (m,n)=(2,3),(3,2),(2,5), or (5,2). Determine all other pairs of integers (m,n) if any, so that () holds for all real numbers x,y,z such that x+y+z=0.

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