IMO Shortlist 1995 problem A2


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 6,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
Let a and b be non-negative integers such that ab \geq c^2, where c is an integer. Prove that there is a number n and integers x_1, x_2, \ldots, x_n, y_1, y_2, \ldots, y_n such that

\sum^n_{i=1} x^2_i = a, \sum^n_{i=1} y^2_i = b, \text{ and } \sum^n_{i=1} x_iy_i = c.
Izvor: Međunarodna matematička olimpijada, shortlist 1995