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a^n + b^n + c^n >= ab^{n-1} + bc^{n-1} + ca^{n-1}

Source: 1975 Swedish Mathematical Competition p3

March 26, 2021
algebrainequalities

Problem Statement

Show that an+bn+cn≥abn−1+bcn−1+can−1 a^n + b^n + c^n \geq ab^{n-1} + bc^{n-1} + ca^{n-1} for real a,b,c≥0a,b,c \geq 0 and nn a positive integer.
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