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Inequality about power sum

Source: 2019 China TST Test 4 P5

April 5, 2019
inequalitiesChina TSTChina

Problem Statement

Find all integer nn such that the following property holds: for any positive real numbers a,b,c,x,y,za,b,c,x,y,z, with max(a,b,c,x,y,z)=amax(a,b,c,x,y,z)=a , a+b+c=x+y+za+b+c=x+y+z and abc=xyzabc=xyz, the inequality an+bn+cn≥xn+yn+zna^n+b^n+c^n \ge x^n+y^n+z^n holds.
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