3

Part of 2007 Hanoi Open Mathematics Competitions

Problems(2)

possible number of diagonals of a convex polygon (HOMC 2007 J Q3)

Source:

Which of the following is a possible number of diagonals of a convex polygon?
(A)

02

21

32

54

63

geometrydiagonals

Source:

Find the number of dierent positive integer triples (x; y; z) satsfying the equations x+y-z=1 and

x^2+y^2-z^2=1