MathDB
9th ibmo - brazil 1994/q1.

Source: Spanish Communities

May 7, 2006
number theory unsolvednumber theory

Problem Statement

A number nn is said to be nice if it exists an integer r>0r>0 such that the expression of nn in base rr has all its digits equal. For example, 62 and 15 are \emph{nice} because 62 is 222 in base 5, and 15 is 33 in base 4. Show that 1993 is not nice, but 1994 is.