MathDB

2

Part of 2008 Bundeswettbewerb Mathematik

Problems(2)

Addition of the reciprocals of the summands yield 1

Source: Germany Bundeswettbewerb Mathematik 2008, Round 1, Problem 2

7/19/2008
Represent the number 2008 2008 as a sum of natural number such that the addition of the reciprocals of the summands yield 1.
FTWalgebra unsolvedalgebra
Positive integers a,b,c have a common divisor greater than 1

Source: Germany Bundeswettbewerb Mathematik 2008, Round 2, Problem 2

9/7/2008
Let the positive integers a,b,c a,b,c chosen such that the quotients \frac{bc}{b\plus{}c}, \frac{ca}{c\plus{}a} and \frac{ab}{a\plus{}b} are integers. Prove that a,b,c a,b,c have a common divisor greater than 1.
inequalitiesnumber theorygreatest common divisorleast common multiplerelatively primenumber theory unsolved