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3

Part of 2012 IMC

Problems(2)

IMC 2012 Day 1, Problem 3

Source:

7/28/2012
Given an integer n>1n>1, let SnS_n be the group of permutations of the numbers 1,  2,  3,  …,  n1,\;2,\;3,\;\ldots,\;n. Two players, A and B, play the following game. Taking turns, they select elements (one element at a time) from the group SnS_n. It is forbidden to select an element that has already been selected. The game ends when the selected elements generate the whole group SnS_n. The player who made the last move loses the game. The first move is made by A. Which player has a winning strategy?
Proposed by Fedor Petrov, St. Petersburg State University.
group theoryabstract algebraIMCcollege contests
n!+1 divides (2012n)!

Source: IMC 2012, Day 2, Problem 3

7/29/2012
Is the set of positive integers nn such that n!+1n!+1 divides (2012n)!(2012n)! finite or infinite?
Proposed by Fedor Petrov, St. Petersburg State University.
logarithmsIMCcollege contests