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1999 KJMO sum, square sum, cubic sum

Source: 1999 KJMO

June 30, 2024
algebrafactorizationsum of cubes

Problem Statement

Three integers are given. AA denotes the sum of the integers, BB denotes the sum of the square of the integers and CC denotes the sum of cubes of the integers(that is, if the three integers are x,y,zx, y, z, then A=x+y+zA=x+y+z, B=x2+y2+z2B=x^2+y^2+z^2, C=x3+y3+z3C=x^3+y^3+z^3). If 9A≥B+609A \geq B+60 and C≥360C \geq 360, find A,B,CA, B, C.
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