Home Competitions AUSTRIAN-POLISH 1995 Problem 9
AUSTRIAN-POLISH 1995 Problem 9
Prove that for all positive integers n , m n,m n , m x , y > 0 x, y > 0 x , y > 0 ( n − 1 ) ( m − 1 ) ( x n + m + y n + m ) + ( n + m − 1 ) ( x n y m + x m y n ) ≥ n m ( x n + m − 1 y + x y n + m − 1 ) . (n - 1)(m- 1)(x^{n+m} + y^{n+m}) + (n + m - 1)(x^ny^m + x^my^n) \ge
nm(x^{n+m-1}y + xy^{n+m-1}). ( n − 1 ) ( m − 1 ) ( x n + m + y n + m ) + ( n + m − 1 ) ( x n y m + x m y n ) ≥ nm ( x n + m − 1 y + x y n + m − 1 ) .
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