1990 IMO Problems/Problem 5
5. Given an initial integer , two players,
and
, choose integers
, . . . alternately according to the following rules:
Knowing
,
chooses any integer
such that
.
Knowing
,
chooses any integer
such that
is a prime raised to a positive integer power.
Player
wins the game by choosing the number 1990; player
wins by choosing
the number 1. For which
does:
(a)
have a winning strategy?
(b)
have a winning strategy?
(c) Neither player have a winning strategy?