A proper edge t-coloring of a graph is a coloring of its edges with colors 1, 2, ..., t such that all colors are used, and no two adjacent edges receive the same color. For any integer n ≥ 3, all possible values of t are found, for which there exists such a proper edge t-coloring of the simple cycle C(n), which uses for each pair of adjacent edges either consecutive colors or the first and the ...