Before trying the problem "note your opinion as to whether the observed pattern is known to continue, known not to continue, or not known at all."
For integers greater than 1,
2n is never congruent to 1 (mod n)
2n is congruent to 2 (mod n) whenever n is prime, and sometimes when it isn't,
is 2n ever congruent to 3 (mod n)?
Find the smallest positive integer that is a multiple of 35 whose digits are all the same.