MathDB

2

Part of 2005 Pan African

Problems(2)

Integer set and polynomial

Source: Pan African Maths Olympiad

8/11/2005
Let SS be a set of integers with the property that any integer root of any non-zero polynomial with coefficients in SS also belongs to SS. If 00 and 10001000 are elements of SS, prove that āˆ’2-2 is also an element of SS.
algebrapolynomial
Animal and Cage

Source: Pan African Maths Olympiad

8/11/2005
Noah has to fit 8 species of animals into 4 cages of the Arc. He planes to put two species of animal in each cage. It turns out that, for each species of animal, there are at most 3 other species with which it cannot share a cage. Prove that there is a way to assign the animals to the cages so that each species shares a cage with a compatible species.
Euleralgorithmunsolved