Equichordal point

In 1916 Fujiwara proposed the question of whether a curve could have two equichordal points (offering in the same paper a proof that three or more is impossible).

Independently, a year later, Blaschke, Rothe and Weitzenböck posed the same question.

[3] The problem remained unsolved until it was finally proven impossible in 1996 by Marek Rychlik.

[4][5] Despite its elementary formulation, the equichordal point problem was difficult to solve.

Rychlik's theorem is proved by methods of advanced complex analysis and algebraic geometry and it is 72 pages long.