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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

Answer published by the source. Consult the official source to check your work against its answer.

problem

Find all positive integers

a

such that there exists a set

X

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

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: 2
config / split: / test

Official source

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