Titlebook: Exploring, Investigating and Discovering in Mathematics; Vasile Berinde Textbook 2004 Springer Basel AG 2004 Algebra.Applied Mathematics.A

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Sequences of Integers Simultaneously Prime,In this section we design a universal algorithm for solving various problems included in the class mentioned in the title of the section. Then we shall use it in exploring the set of solutions for one special problem of this class. At least two reasons are behind our approach

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Solving Some Cyclic Systems,A system of the form.is called cyclic if, by any circular permutation of its unknowns.the system does not change. The symmetric systems of two equations and two unknowns are the most simple examples of cyclic systems.

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On a Property of Recurrent Affine Sequences,In the present section we shall give a characterization of convergent sequences of real numbers, by means of affine combinations of.successive terms..2). In this way we shall survey some known results and add other similar related problems.

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Exponential Equations Having Exactly Two Solutions,The starting point of all investigations and explorations in this section is..

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An Extension of the Leibniz-Newton Formula,In this section we are going to present a slight extension of the Leibniz-Newton formula for the computation of the definite integral, an extension that can be applied also in the case of some integrable functions which do not admit primitives

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A Measurement Problem,In some books on recreational mathematics, but also in mathematics journals and school competitions, one can sometimes meet problems asking to find a certain quantity (mass, volume), without using a standard measurement unit. A problem of this kind is the source problem of this section.

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