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Russia 2003,hard

Source: help me

November 10, 2009
functionnumber theory unsolvednumber theory

Problem Statement

Let a0 a_0 be a natural number. The sequence (an) (a_n) is defined by a_{n\plus{}1}\equal{}\frac{a_n}{5} if an a_n is divisible by 5 5 and a_{n\plus{}1}\equal{}[a_n \sqrt{5}] otherwise . Show that the sequence an a_n is increasing starting from some term.
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