Knots and Pythagorean Triangles

There are equally spaced 1212 knots in the loop of string in Figure-1. This string loop can be transformed into Figure-2, which is a right triangle with a knot on each of its vertices.

Does this same transformation work for any other number of knots k12k\neq12?

Find the minimum k>12k>12.
If there is no such k>12k>12, enter 0.

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