N4

Part of 2018 Pan-African Shortlist

Problems(1)

Divisibility of natural numbers containing each digit from $1$ to $7$

Source: 2018 Pan-African Shortlist - N4

S

49

n

, with the property that each of the digits

1, 2, 3, \dots, 7

appears in the decimal expansion of

n

seven times (and

8, 9

0

do not appear). Show that no two distinct elements of

S

divide each other.

number theoryDivisibilityDigits