It is referenced that in 


Chowla, S., *Proof of a conjecture of Julia Robinson*, Norske Vid. Selsk. Forh. (Trondheim) 34, 100–101 (1961),


it is shown that the equation $\epsilon\_1 + \epsilon\_2 = 1$ has only finitely many solutions, when $\epsilon\_1, \epsilon\_2$ are units of a given number field. Unfortunately, the article seems to be unavailable electronically. I hence wonder if the argument given in the article is available from another source or if it could be reproduced here, if not too lengthy.


Thank you.



An old paper of S.Chowla on unit equations
This is a standard result, and is true for $S$-units. It is proven in many texts, although sometimes the reader is referred elsewhere for the estimate from Diophantine approximation that is needed (such as Thue's or Roth's theorem). The full proof is contained in my book with Hindry, *Diophantine Geometry*, GTM 201, Springer, Section D.8 (Application: The Unit Equation $U+V=1$). The reduction of the unit equation to Diophantine approximation is in my elliptic curves book (and in many many other books). There are also quantitative results (upper bounds for the number of solutions) and effective results (upper bounds for the largest solution, using linear forms in logs).


