Question 5
It is claimed that the number
$$N=526315789473684210$$
is a persistent number, that is, if multiplied by any positive integer the resulting number always contains the ten digits $0,1,\ldots,9$ in some order with possible repetitions.
(a) Prove or disprove the claim.
(b) Are there any persistent numbers smaller than the above number?
$$N=526315789473684210$$
is a persistent number, that is, if multiplied by any positive integer the resulting number always contains the ten digits $0,1,\ldots,9$ in some order with possible repetitions.
(a) Prove or disprove the claim.
(b) Are there any persistent numbers smaller than the above number?