., an, b 21 ..., b n determined by the relations p n = a n pn-1 + b n pn-2, qn = a ngn -1 + bngn-2, with the conditions p1= at, q 2 = a2, q, = 1, 0) =0, have been studied under the name of continuants.

qn= k l a2, a3,, an The theory of continuants is due in the first place to Euler.

The reader will find the theory completely treated in Chrystal's Algebra, where will be found the exhibition of a prime number of the form 4p+I as the actual sum of two squares by means of continuants, a result given by H.

determinant a1 - I a2 O -I o 0 u an bn O O - - o o -I a n, from which point of view continuants have been treated by W.