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May 16, 2014 at 20:45 comment added Eric Rowell I am aware of the result of Evertse and others showing that there are finitely many solutions, even in the case of number fields. I want to find all solutions if possible.
May 16, 2014 at 19:01 history edited Eric Rowell CC BY-SA 3.0
deleted 3 characters in body
May 16, 2014 at 17:41 comment added Felipe Voloch S-integers in the usual sense are allowed any integer numerators. What you are talking about is, I think, S-units. The S-unit equation (sum of S-units = 1) has been studied a lot with the main result being finiteness of solutions (modulo obvious conditions). You still haven't stated a question.
May 16, 2014 at 17:37 comment added Eric Rowell If someone has studied the problem for S-integers then this will help as I can clear denominators. I have added a ? and a tag to make it clearer.
May 16, 2014 at 17:36 history edited Eric Rowell CC BY-SA 3.0
added a tag and a question mark.
May 16, 2014 at 15:37 comment added Felipe Voloch S-integers usually mean rational numbers with denominators divisible only by primes in S. That is not what you are talking about in the body of your question. Also, what is the question?
May 16, 2014 at 14:47 history asked Eric Rowell CC BY-SA 3.0