Prove that there are infinitely many positive integers n wit

Prove that there are infinitely many positive integers n with the following two properties: All of the digits of n in base 10 are 1

Since, we have given to prove that there are infinite number of integers whose base is 10 is 1 but divisible by 49

suppose, let\'s assume 3 digit integers

three digit integer : a1b

100a+10+b=980(maximum 49 multiple in two digits)

100a +b =970....which is not possible because (a and b lies between 0 and 9)

let\'s take four digits

four digits number: ab1c

1000a+100b+10+c=9996..(maximum four digit number which is multiple of 49)

1000a+100b+c=9886

So, there can be various possible values of \'a\' and \'b\' and \'c\'

For example:

1519 is multiple of 49 ...whose 10th base is 1

1617 is multiple of 49 ...whose 10th base is 1

1715 is multiple of 49 ...whose 10th base is 1

and many more

Similarly , there can be various value is possible if we take five digit numbers

and in six digits numbers

Hence , there infinitely many positive integers n with the digits of n in base 10 are 1