Let a,b be positive real numbers. For any positive integer n, denote by xn the sum of digits of the number [an+b] in it's decimal representation. Show that the sequence (xn)n≥1 contains a constant subsequence. Laurentiu Panaitopol
Source: Romanian TST 2002
Tags: pigeonhole principle, number theory proposed, number theory
Let a,b be positive real numbers. For any positive integer n, denote by xn the sum of digits of the number [an+b] in it's decimal representation. Show that the sequence (xn)n≥1 contains a constant subsequence. Laurentiu Panaitopol