We let L denote the length of the period of the continued fraction expansion

Let p be a prime ≡ 1 (mod 4) such that the norm of the fundamental unit of Q(√2p) is −1. A necessary and sufficient condition is given for A to be larger than B in the representation p = A2 +B2, A ≡ 1 (mod 2), B ≡ 0 (mod 2), A> 0, B> 0. Let p be a prime with p ≡ 1 (mod 4). It is a classical result that there exist unique positive integers A and B such that p = A2 +B2, A ≡ 1 (mod 2), B ≡ 0 (mod 2). (1) We consider the problem of giving a necessary and sufficient condition for A to be larger than B. By making use of results of Kaplan and Williams [2], we are able to solve this problem when the norm of the fundamental uni