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x_n is the sum of digits of the number [an+b]

Source: Romanian TST 2002

February 5, 2011
pigeonhole principlenumber theory proposednumber theory

Problem Statement

Let a,ba,b be positive real numbers. For any positive integer nn, denote by xnx_n the sum of digits of the number [an+b][an+b] in it's decimal representation. Show that the sequence (xn)n≥1(x_n)_{n\ge 1} contains a constant subsequence.
Laurentiu Panaitopol
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