MathDB
ASU 455 All Soviet Union MO 1987 game with naturals <=p

Source:

August 7, 2019
gamegame strategycombinatorics

Problem Statement

Two players are writting in turn natural numbers not exceeding pp. The rules forbid to write the divisors of the numbers already having been written. Those who cannot make his move looses.
a) Who, and how, can win if p=10p=10?
b) Who wins if p=1000p=1000?