Question

Let p be a prime number, different from 2 and 5. show that there exists a natural number whose decimal writing contains only the digit 1 (that is a number in the list 1, 11, 111, 1111, etc.) which is divisible by p.

Answer 1

Let p be a prime number, different from 2 and 5. show that there exists a natural number whose decimal writing contains only the digit 1 (that is a number in the list 1, 11, 111, 1111, etc.) which is divisible by p.×11111.1111