Bourbaki

Exercise 3, § 2

Functions of a Real Variable, VI, 292

Show that, for every integer p>1p > 1,

Bn(xp)+Bn(x+1p)+⋯+Bn(x+p−1p)=1pn−1Bn(X). B_n \left( \frac{x}{p} \right) + B_n \left( \frac{x+1}{p} \right) + \cdots + B_n \left( \frac{x+p-1}{p} \right) = \frac{1}{p^{n-1}} B_n(X).
Solution

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Transcribed from the printed volume. Not translated.