Sloane A020348 indicates the smallest positive integer with continued fraction having a period of 8 is 31 followed by 44, 69, 71, 91, 92, 108, 135, 153, and onward. As the problem asks for the smallest
3digit positive integer, this then would be the positive integer
108.

Posted by Dej Mar
on 20141004 11:53:47 