MathDB

1

Part of 2007 Tuymaada Olympiad

Problems(2)

more like trivial colouring exercise

Source: Tuymaada 2007, Problem 5

7/15/2007
What minimum number of colours is sufficient to colour all positive real numbers so that every two numbers whose ratio is 4 or 8 have different colours?
ratiologarithmsmodular arithmeticcombinatorics proposedcombinatorics
classic divisibility..

Source: Tuymaada 2007, Problem 1

7/15/2007
Positive integers a<b a<b are given. Prove that among every b b consecutive positive integers there are two numbers whose product is divisible by ab ab.
number theory proposednumber theory