MathDB
Persistent Numbers

Source:

March 10, 2007

Problem Statement

In a non-recent edition of Ripley's Believe It or Not, it was stated that the number N=526315789473684210N = 526315789473684210 is a persistent number, that is, if multiplied by any positive integer the resulting number always contains the ten digits 0,1,2,3,...,8,90, 1, 2, 3,..., 8, 9 in some order with possible repetitions. a) Prove or disprove the above statement. b) Are there any persistent numbers smaller than the above number?