MathDB
Tuymaada 2002

Source:

January 22, 2007
calculusintegrationfloor functionpigeonhole principlenumber theory unsolvednumber theory

Problem Statement

A real number aa is given. The sequence n1<n2<n3<...n_{1}< n_{2}< n_{3}< ... consists of all the positive integral nn such that {na}<110\{na\}< \frac{1}{10}. Prove that there are at most three different numbers among the numbers n2−n1n_{2}-n_{1}, n3−n2n_{3}-n_{2}, n4−n3n_{4}-n_{3}, …\ldots.
A corollary of a theorem from ergodic theory
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