IMO 1969 LL SWE59

For each \lambda (0 < \lambda < 1 and \lambda ̸= 1/n for all n = 1, 2, 3, . . .)

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IMO 1969 LL SWE59

Origin: SWE

Problem

For each \lambda (0 < \lambda < 1 and \lambda ̸= 1/n for all n = 1, 2, 3, . . .) construct a continuous function f such that there do not exist x, y with 0 < \lambda < y = x + \lambda \leq1 for which f(x) = f(y).