MathDB

Let

d

be a natural number. Given two natural numbers

M

and

N

with

d

digits,

M

is a friend of

N

if and only if the

d

numbers obtained substituting each one of the digits of

M

by the digit of

N

which is on the same position are all multiples of

7

. Find all the values of

d

for which the following condition is valid: For any two numbers

M

and

N

with

d

digits,

M

is a friend of

N

if and only if

N

is a friend of

M

3