MathDB

3

Part of 2009 Cuba MO

Problems(2)

Inca nxn board

Source: 2009 Cuba MO 1.3

8/27/2024
In each square of an n×nn \times n board with n≥2n\ge 2, an integer is written not null. Said board is called Inca if for each square, the number written on it is equal to the difference of the numbers written on two of its neighboring squares (with a common side). For what values of nn, can you get Inca boards ?
combinatorics
min x^2 + y^2 + z^2 if x^3 + y^3 + z^3 -3xyz = 1

Source: 2009 Cuba 2.3

8/27/2024
Determine the smallest value of x2+y2+z2x^2 + y^2 + z^2, where x,y,zx, y, z are real numbers, so that x3+y3+z3−3xyz=1.x^3 + y^3 + z^3 -3xyz = 1.
algebrainequalities