On square triangular number / Danny Riel P. Barachina

Thesis (Master of Science in Mathematics) -- Eulogio Amang Rodriguez Institute of Science and Technology, 2023

In number theory, a square triangular number is a number
that is both a perfect square and triangular in nature. There
are infinitely many square triangular numbers. To find any
square triangular number, several proof and identities are
discussed in this study.
The proof of each property of square triangular numbers
are provided together with precise illustration of each
property. Proofs are analytical in nature and are
concentrated in providing significant results when applied.
Generation of square triangular numbers in connection
with recurrence relation and Binet's Formula is established.
Different properties of square triangular numbers are also given
that there in complete details and with precision to show
significant formulas being used to prove and propositions.
This paper sought the are several theorems relationship of square
triangular numbers to generating functions, Perfect Square numbers, and Pell's Equation.
With regard to the forgoing goal, it is shown that there
are other numbers related to Square Triangular Numbers such
as Pell and Pell - Lucas Numbers. Relationship with these
numbers is shown in precise manner and several proofs of
these relationships are established.