Ergodicity of \(p\)-adic multiplications and the distribution of Fibonacci numbers (Q2735111)

The ergodic decomposition of the (additive Haar) measure-preserving transformation \(x\mapsto\lambda x\) on the multiplicative group of units in the \(p\)-adic integers is found, and this is used to give an arithmetical characterisation of ergodicity. These results are used to give a very complete description of the distribution modulo prime powers of the Fibonacci numbers (and other second-order linear recurrence sequences).NEWLINENEWLINEFor the entire collection see [Zbl 0961.00011].