MathDB

Let

n>100

be a positive integer and originally the number

1

is written on the blackboard. Petya and Vasya play the following game: every minute Petya represents the number of the board as a sum of two distinct positive fractions with coprime nominator and denominator and Vasya chooses which one to delete. Show that Petya can play in such a manner, that after

n

moves, the denominator of the fraction left on the board is at most

2^n+50

, no matter how Vasya acts.

Problem Statement