14 d (including d = 2)  and that every solution has the form ± ( x$_{n}$  y$_{n}$ ) where x$_{n}$ + √$_{dy}$$_{n}$ = ( x$_{1}$ $_{+}$√$_{dy}$$_{1}$$_{)}$ n for some solution ( x$_{1}$  y$_{1}$ ) and n ∈ Z . Acknowledgment Many thanks to Professor Dan Segal  All-Souls College  Oxford  for his advice. References [1] Borevich  Z. I.  and Shafarevich I. R.  Number Theory  Academic Press  New York  1973. [2] C. S. Dalawat  Primary units in cyclotomic fields  Annales des sciences math´ ematiques du Qu´ ebec to appear  2011. [3] G. L. Dirichlet  Sur la mani`ere de r´esoudre l’´equation t 2 − pu 2 = 1 au moyen des fonctions circulaires  Journal f¨ ur die reine und angewandte Mathematik 17  pp. 286-290  1837. [4] V. Flynn  Algebraic Number Theory Lecture Notes . University of Oxford. Oxford Mathematical Institute  Oxford  UK. 2011. Lecture Notes. [5] K. Ireland and M. Rosen  A Classical Introduction to Modern Number Theory  Springer-Verlag  New York  1982. [6] S. Lang  Algebraic Number Theory  Springer-Verlag  New York  1986. [7] L. C. Washington  Introduction to Cyclotomic Fields  Springer-Verlag  New York  1982. KABALAN GASPARD