On the blackboard are written the 2003 integers from 1 to 2003. Lucas must delete 90 numbers. Next, Mauro must choose 37 from the numbers that remain written. If the 37 numbers Mauro chooses form an arithmetic progression, Mauro wins. If not, Lucas wins. Decide if Lucas can choose the 90 numbers he erases so that victory is assured.
combinatoricsnumber theoryalgebra