MathDB
czech republic,czech and slovakia MO(third round),2008 p4

Source:

February 25, 2012
modular arithmeticcalculusnumber theory proposednumber theory

Problem Statement

In decimal representation, we call an integer kk-carboxylic if and only if it can be represented as a sum of kk distinct integers, all of them greater than 99, whose digits are the same. For instance, 20082008 is 55-carboxylic because 2008=1111+666+99+88+442008=1111+666+99+88+44. Find, with an example, the smallest integer kk such that 80028002 is kk-carboxylic.