3

Part of 1994 Turkey Team Selection Test

Problems(2)

Turkey TST 1994 - P3

Source:

All sides and diagonals of a

25

-gon are drawn either red or white. Show that at least

500

triangles, having all three sides are in same color and having all three vertices from the vertices of the

25

-gon, can be found.

combinatorics proposedcombinatorics

Turkey TST 1994 - P6

Source:

Find all integer pairs

(a,b)

a\cdot b

a^2+b^2+3

algebrapolynomialVietaquadraticsnumber theory proposednumber theory