2014 USAJMO Problems/Problem 4

Revision as of 17:42, 30 April 2014 by TheMaskedMagician (talk | contribs) (Created page with "==Problem== Let <math>b\geq 2</math> be an integer, and let <math>s_b(n)</math> denote the sum of the digits of <math>n</math> when it is written in base <math>b</math>. Show th...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $b\geq 2$ be an integer, and let $s_b(n)$ denote the sum of the digits of $n$ when it is written in base $b$. Show that there are infinitely many positive integers that cannot be represented in the form $n+s_b(n)$, where $n$ is a positive integer.

Solution