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Omni-MATH / Find all positive integers a such that there exists a set X of 6 integers satisfying the following conditions: for every k=1,2,…,36 there exist x,y∈X such that ax+y−k is divisible …

Problem

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problem

Find all positive integers aa such that there exists a set XX of 66 integers satisfying the following conditions: for every k=1,2,…,36k=1,2,\ldots ,36 there exist x,y∈Xx,y\in X such that ax+y−kax+y-k is divisible by 3737.
Plain-text mathematical notation (without MathML)
Find all positive integers a such that there exists a set X of 6 integers satisfying the following conditions: for every k=1,2,…,36 there exist x,y∈X such that ax+y−k is divisible by 37.
Original LaTeX notation
Find all positive integers $a$ such that there exists a set $X$ of $6$ integers satisfying the following conditions: for every $k=1,2,\ldots ,36$ there exist $x,y\in X$ such that $ax+y-k$ is divisible by $37$.

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Source and history

task_id
062dbf81-70a5-5fa8-b8b7-555fbdef3d41
task_key
test--062dbf81-70a5-5fa8-b8b7-555fbdef3d41
task_revision_id
5
config / split
/ test

Official source

initial import