IMO 2017 Shortlist N4
Call a rational number short if it has nitely many digits in its de imal expansion. For a positive integer m, we say th...
Category: Number Theory
Problem
Call a rational number short if it has nitely many digits in its de imal expansion. For a positive integer m, we say that a positive integer t is m-tasti if there exists a number c P t1,2,3,...,2017u su h that 10t ´ 1 c ¨ m is short, and su h that 10k ´ 1 c ¨ m is not short for any 1 ď k ă t. Let Spmq be the set of m-tasti numbers. Consider Spmq for m “ 1,2,.... What is the maximum number of elements in Spmq? (Turkey)