Find the smallest value of a 3-digit positive integer N such that continued fraction for √N has period 8.

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 3-digit positive integer, this then would be the positive integer 108.

Posted by Dej Mar on 2014-10-04 11:53:47