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Omni-MATH / Does there exist a finite set A of positive integers of at least two elements and an infinite set B of positive integers, such that any two distinct elements in A+B are coprime, an…

Problem

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problem

Does there exist a finite set

A

of positive integers of at least two elements and an infinite set

B

of positive integers, such that any two distinct elements in

A+B

are coprime, and for any coprime positive integers

m,n

, there exists an element

x

A+B

satisfying $x\equiv n \pmod m$ ? Here

A+B=\{a+b|a\in A, b\in B\}

Plain-text mathematical notation (without MathML)

Does there exist a finite set A of positive integers of at least two elements and an infinite set B of positive integers, such that any two distinct elements in A+B are coprime, and for any coprime positive integers m,n, there exists an element x in A+B satisfying $x\equiv n \pmod m$ ?

Here A+B={a+b|a∈A,b∈B}.

Original LaTeX notation

Does there exist a finite set $A$ of positive integers of at least two elements and an infinite set $B$ of positive integers, such that any two distinct elements in $A+B$ are coprime, and for any coprime positive integers $m,n$, there exists an element $x$ in $A+B$ satisfying $x\equiv n \pmod m$ ?

Here $A+B=\{a+b|a\in A, b\in B\}$.

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task_id: 5ab1bb8f-6380-5cce-841b-9cfff532242a
task_key: test--5ab1bb8f-6380-5cce-841b-9cfff532242a
task_revision_id: 3
config / split: / test

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