Let r and k be positive integers such that all prime divisors of r are greater than 50.A positive integer, whose decimal representation (without leading zeroes) has at least k digits, will be called nice if every sequence of k consecutive digits of this decimal representation forms a number (possibly with leading zeroes) which is a multiple of r.Prove that if there exist infinitely many nice numbers, then the number 10kā1 is nice as well. number theory proposednumber theory