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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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Combining coefficients in a sum of inequalities

In an induction proof of a lemma I would like to prove the following statement. Let $U$ be a non-empty finite set and let $X_{i,j}$ for all $i\not=j \in U$ be real numbers. Assume for each $j\in U$ we …
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