MathDB

Given two positive integers

n

and

k

, we say that

k

n

-ergetic if: However the elements of

M=\{1,2,\ldots, k\}

are coloured in red and green, there exist

n

not necessarily distinct integers of the same colour whose sum is again an element of

M

of the same colour. For each positive integer

n

, determine the least

n

-ergetic integer, if it exists.

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