A fifty digit positive integer satisfies all these given conditions:

1. The number is constituted entirely by the digit 1 with the exception of the units digit.
2. The number is divisible by 53.

Determine the units digit.

Extra Challenge: Solve this puzzle without using a computer-assisted method.

(In reply to computer solution by Charlie)

Since 9 and 53 don't share a factor you can still skip the computer:

Posted by xdog on 2022-05-05 15:31:06