Theorem 2, at the end of Section 2, was not originally obtained in the manner indicated there.
A key step in obtaining (6) is Hölder's inequality.
We thus obtain f=g. [Not: “We obtain that f=g'', “We receive f=g''.]
Also, wherever possible, we work with integer coefficients, enabling us to obtain information about torsion.
the solution obtained [Not: “the obtained solution'']