Question

If there is natural number n relative prime with 10. Then show that there exist another natural number m such that all digits are 1's and m is div. by 'n'.

Answer 1

Let $m=1$

Co prime numbers are these, it

the only positive integer that

divides both of them is 1 so,

m cannot be 1

Let $m=11$

Only numbers that divides 11 is 1

So, m cannot be 11

Let $m=111$

m is divisible by 3 must all digits

are not 1

Let $m=1111$

m is dissoluble by 11 which is

Co prime with 10

So $m=1111$ or $11.11$