Savannah State University

Title 1
Conquering Perfect Numbers Using the Tool of Finite Series

Synopsis 1
Mathematicians and non-mathematicians have been fascinated for centuries by the properties and patterns of numbers. They have noticed that some numbers are equal to the sum of all of their factors (not including the number itself). Such numbers are called perfect numbers. Thus a positive integer is called a perfect number if it is equal to the sum of its proper positive divisors. The search for perfect numbers began in ancient times.

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Title 2
The Double Angle Formula of the Mulatu Numbers

Synopsis 2
The Mulatu numbers were introduced in [1] . The numbers are sequences of numbers of the form: 4,1, 5,6,11,17,28,45… The numbers have wonderful and amazing properties and patterns.

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Title 3
The Mathematical Beauty Of Triangular Numbers

Synopsis 3
1+2+3+4+5+6+7….+n [2]. In other words, triangular numbers are those counting numbers that can be written as n T = 1+2+3+…+ n. So,

T1= 1
T2= 1+2=3
T3= 1+2+3=6
T4= 1+2+3+4=10
T5= 1+2+3+4+5=15
T6= 1+2+3+4+5+6= 21
T7= 1+2+3+4+5+6+7= 28
T8= 1+2+3+4+5+6+7+8= 36
T10 =1+2+3+4+5+6+7+8+9+10=55

In this paper we investigate some important properties of triangular numbers. Some important results dealing with the mathematical concept of triangular numbers will be proved. We try our best to give short and readable proofs. Most of the results are supplemented with examples.

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