MathDB

1

Part of 2000 239 Open Mathematical Olympiad

Problems(2)

$ xy + yz + zt = xt $ then the sum of squares of some two

Source: 239 2000 J2

5/17/2020
Given pairwise coprime natural numbers x x , y y , z z , t t such that xy+yz+zt=xt xy + yz + zt = xt . Prove that the sum of the squares of some two of these numbers is twice the sum of the squares of the two remaining.
number theory
Rearranging Chips on Infinite Plane

Source: 239 2000 J1

5/17/2020
On an infinite checkered plane 100100 chips in form of a 10×1010\times 10 square are given. These chips are rearranged such that any two adjacent (by side) chips are again adjacent, moreover no two chips are in the same cell. Prove that the chips are again in form of a square.
combinatorics