MathDB

The squares of an infinite chessboard are numbered

1,2,\ldots

along a spiral, as shown in the picture. A rightline is the sequence of the numbers in the squares obtained by starting at one square at going to the right. a) Prove that exists a rightline without multiples of

3

. b) Prove that there are infinitely many pairwise disjoint rightlines not containing multiples of

3

Problem Statement