The squares of an infinite chessboard are numbered 1,2,… 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. combinatorics proposedcombinatorics