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Omni-MATH / Two players play the following game: there are two heaps of tokens, and they…

Problem

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problem

Two players play the following game: there are two heaps of tokens, and they take turns to pick some tokens from them. The winner of the game is the player who takes away the last token. If the number of tokens in the two heaps are AA and BB at a given moment, the player whose turn it is can take away a number of tokens that is a multiple of AA or a multiple of BB from one of the heaps. Find those pair of integers (k,n)(k,n) for which the second player has a winning strategy, if the initial number of tokens is kk in the first heap and nn in the second heap.
Plain-text mathematical notation (without MathML)
Two players play the following game: there are two heaps of tokens, and they take turns to pick some tokens from them. The winner of the game is the player who takes away the last token. If the number of tokens in the two heaps are A and B at a given moment, the player whose turn it is can take away a number of tokens that is a multiple of A or a multiple of B from one of the heaps.

Find those pair of integers (k,n) for which the second player has a winning strategy, if the initial number of tokens is k in the first heap and n in the second heap.
Original LaTeX notation
Two players play the following game: there are two heaps of tokens, and they take turns to pick some tokens from them. The winner of the game is the player who takes away the last token. If the number of tokens in the two heaps are $A$ and $B$ at a given moment, the player whose turn it is can take away a number of tokens that is a multiple of $A$ or a multiple of $B$ from one of the heaps.

Find those pair of integers $(k,n)$ for which the second player has a winning strategy, if the initial number of tokens is $k$ in the first heap and $n$ in the second heap.

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Source and history

task_id
e559fe04-bb9d-5bd8-a6e5-e9076f103630
task_key
test--e559fe04-bb9d-5bd8-a6e5-e9076f103630
task_revision_id
1
config / split
/ test

Official source

initial import