MathDB

2

Part of 2000 Bundeswettbewerb Mathematik

Problems(2)

a+b is divisible by a-b [Germany BW 2000]

Source:

2/3/2011
Prove that for every integer n≥2n \geq 2 there exist nn different positive integers such that for any two of these integers aa and bb their sum a+ba+b is divisible by their difference a−b.a - b.
number theory proposednumber theory
5-tuple with property sum of any 3 is divisible by the sum of the other 2

Source: 2000 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p2

1/27/2020
A 55-tuple (1,1,1,1,2)(1,1,1,1,2) has the property that the sum of any three of them is divisible by the sum of the remaining two. Is there a 55-tuple with this property whose all terms are distinct?
number theorySumdivisible