Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  develop a new method for finding all perfect pors which can be expressed as the sum of two rational S-units, where S is a finite set of primes. Our approach is based upon the modularity of Galois representations and, for the most part, does not require lor bounds for linear forms in logarithms. Its main virtue is that it enables to carry out such a program explicitly, at least for certain small sets of primes S;  do so for S = {2, 3} and S = {3, 5, 7}.
['Michael A. Bennett', 'Nicolas Billerey']
I am writing a research paper on a idea Sums of two ${s}$-units via frey-hellegouarch curves
[{"from": "human", "value": "I am writing a research paper on a idea Sums of two ${s}$-units via frey-hellegouarch curves"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  develop a new method for finding all perfect pors which can be expressed as the sum of two rational S-units, where S is a finite set of primes. Our approach is based upon the modularity of Galois representations and, for the most part, does not require lor bounds for linear forms in logarithms. Its main virtue is that it enables to carry out such a program explicitly, at least for certain small sets of primes S;  do so for S = {2, 3} and S = {3, 5, 7}."}]