Kvant Math Problem 2632
Working
Verified: no
Verdicts: FAIL + FAIL
Solve time: 32m22s
Source on kvant.digital
Problem
Petya and Vasya take turns writing fractions of the form $\dfrac1n$ on the board, where $n$ is a positive integer. Petya moves first. On each turn Petya writes only one fraction, while Vasya writes one fraction on his first turn, two fractions on his second turn, and so on, writing one more fraction on each successive turn. Vasya wants the sum of all fractions on the board to be a positive integer after some turn. Can Petya prevent this?
A. Arzhantsev
Tournament of Towns (XLII)
Working