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Omni-MATH / Let n>0 be an integer. Each face of a regular tetrahedron is painted in one of n colors (the faces are not necessarily painted different colors.) Suppose there are n³ possible colo…

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problem

Let n>0n>0 be an integer. Each face of a regular tetrahedron is painted in one of nn colors (the faces are not necessarily painted different colors.) Suppose there are n3n^{3} possible colorings, where rotations, but not reflections, of the same coloring are considered the same. Find all possible values of nn.
Plain-text mathematical notation (without MathML)
Let n>0 be an integer. Each face of a regular tetrahedron is painted in one of n colors (the faces are not necessarily painted different colors.) Suppose there are n³ possible colorings, where rotations, but not reflections, of the same coloring are considered the same. Find all possible values of n.
Original LaTeX notation
Let $n>0$ be an integer. Each face of a regular tetrahedron is painted in one of $n$ colors (the faces are not necessarily painted different colors.) Suppose there are $n^{3}$ possible colorings, where rotations, but not reflections, of the same coloring are considered the same. Find all possible values of $n$.

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Source and history

task_id
9aeab507-ea7b-5d6a-8c87-5c939be0a5d5
task_key
test--9aeab507-ea7b-5d6a-8c87-5c939be0a5d5
task_revision_id
1
config / split
/ test

Official source

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