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Omni-MATH / Two positive integers p,q∈Z^(+) are given. There is a blackboard with n positive integers written on it. A operation is to choose two same number a,a written on the blackboard, and…

Problem

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problem

Two positive integers

p,q \in \mathbf{Z}^{+}

are given. There is a blackboard with

n

positive integers written on it. A operation is to choose two same number

a,a

written on the blackboard, and replace them with

a+p,a+q

. Determine the smallest

n

so that such operation can go on infinitely.

Plain-text mathematical notation (without MathML)

Two positive integers p,q∈Z^(+) are given. There is a blackboard with n positive integers written on it. A operation is to choose two same number a,a written on the blackboard, and replace them with a+p,a+q. Determine the smallest n so that such operation can go on infinitely.

Original LaTeX notation

Two positive integers $p,q \in \mathbf{Z}^{+}$ are given. There is a blackboard with $n$ positive integers written on it. A operation is to choose two same number $a,a$ written on the blackboard, and replace them with $a+p,a+q$. Determine the smallest $n$ so that such operation can go on infinitely.

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task_id: ec859739-d684-514d-b335-f3616176a9e9
task_key: test--ec859739-d684-514d-b335-f3616176a9e9
task_revision_id: 4
config / split: / test

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