MathDB

Let

n

and

k

be given relatively prime natural numbers,

k<n.

Each number in the set

M=\{1,2,...,n-1\}

is colored either blue or white. It is given that [*] for each

i\in M,

both

i

and

n-i

have the same color, [*] for each

i\in M,i\ne k,

both

i

and

\left \vert i-k \right \vert

have the same color. Prove that all numbers in

M

have the same color.

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