IMO 2022 Shortlist N5
For each 1 ď i ď 9 and T P N, define dipTq to be the total number of times the digit i appears when all the multiples of...
Category: Number Theory
Problem
For each 1 ď i ď 9 and T P N, define dipTq to be the total number of times the digit i appears when all the multiples of 1829 between 1 and T inclusive are written out in base 10. Show that there are infinitely many T P N such that there are precisely two distinct values among d1pTq,d2pTq,...,d9pTq. (United Kingdom)