MathDB

Let integer

n\ge 3,

\tbinom n2

nonnegative real numbers

a_{i,j}

satisfy

a_{i,j}+a_{j,k}\le a_{i,k}

holds for all

1\le i <j<k\le n

. Proof

\left\lfloor\frac{n^2}4\right\rfloor\sum_{1\le i<j\le n}a_{i,j}^4\ge \left(\sum_{1\le i<j\le n}a_{i,j}^2\right)^2.

Proposed by Jingjun Han

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