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Copyright of Journal de Ciencia e Ingeniería is the property of Corporacion Universitaria Autonoma del Cauca and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Pascal's triangle is the simplest triangle containing binomial coefficients and possessing exclusive mathematical properties in it. There are several triangles of numbers exhibiting exotic mathematical oddities. In this paper, we will introduce two number triangles and determine Ramanujan summation related to their entries. In particular, we have proved new results related to Ramanujan summation values of series of odd and even powers of numbers considered from the two number triangles. [ABSTRACT FROM AUTHOR]

The most famous Fibonacci sequence possess a rather easy recurrence relation in which except the first two terms, each term is the sum of two previous terms. In this paper, I try to generalize the recurrence relation of Fibonacci sequence with respect to number of terms as well as considering not just the consecutive terms but terms whose index are in Arithmetic Progression. With this consideration, I try to obtain the limiting ratio of the new sequence produced through such generalization. The answers obtained cover more general class of Fibonacci type sequences and will provide new insights in the discussion of such generalizations. [ABSTRACT FROM AUTHOR]

Diophantine Equations plays a vital role not only in number theory but also in several branches of science. Leonhard Euler was considered to be the most prolific mathematician of all times. In this paper, we will solve one of the problems posed by Euler which turns out to be a Quadratic Diophantine Equation. The method adopted to solve the problem is quite novel and can be generalized for solving similar equations. [ABSTRACT FROM AUTHOR]

Diophantine Equations named after ancient Greek mathematician Diophantus, plays a vital role not only in number theory but also in several branches of science. In this paper, we will solve one of the quadratic Diophantine equations and provide its complete solutions. The method adopted to solve the given equation is using the concept of polar form of a particular complex number. This concept can be generalized for solving similar equations. [ABSTRACT FROM AUTHOR]