MathDB

3

Part of 1992 Polish MO Finals

Problems(2)

divisibility of fractionals

Source: Problem 6, Polish NO 1992

10/1/2005
Show that (k3)!(k^3)! is divisible by (k!)k2+k+1(k!)^{k^2+k+1}.
number theory solvednumber theory
inequality for real numbers and 2 sums

Source: Problem 3, Polish NO 1992

10/1/2005
Show that for real numbers x1,x2,...,xnx_1, x_2, ... , x_n we have: ∑i=1n∑j=1nxixji+j≥0 \sum\limits_{i=1}^n \sum\limits_{j=1}^n \dfrac{x_ix_j}{i+j} \geq 0 When do we have equality?
inequalitiesfunction