MathDB

Peter picked a positive integer, multiplied it by 5, multiplied the result by 5,then multiplied the result by 5 again and so on. Altogether

k

multiplications were made. It so happened that the decimal representations of the original number and of all

k

resulting numbers in this sequence do not contain digit

7

. Prove that there exists a positive integer such that it can be multiplied

k

times by

2

so that no number in this sequence contains digit

7

Problem Statement