Ivan Shishkin, Rye (1878)

Problems/Real analysisUnreviewed

A binomial rigidity

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Let nn be an odd integer with n⩾3n \geqslant 3. Determine all continuous functions f:[0,1]→Rf:[0,1] \rightarrow \mathbb{R} such that, for every k∈{1,…,n−1}k \in\{1, \ldots, n-1\},

∫01(f(x1/k))n−k dx=kn.\int_0^1\left(f\left(x^{1 / k}\right)\right)^{n-k} \mathrm{~d} x=\frac{k}{n} .

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  1. Oral ENS 2025
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