Barachina, Danny Riel P.  <br/><br/>
On square triangular number 
/ Danny Riel P. Barachina 
 - Sampaloc, Manila   : Eulogio Amang Rodriguez Institute of Science and Technology  ,2023. 
 - ix; 151 leaves   ; 27 x 21cm.  
<br/><br/> Thesis (Master of Science in Mathematics) -- Eulogio Amang Rodriguez Institute of Science and Technology, 2023 
<br/><br/> In number theory, a square triangular number is a number<br/>that is both a perfect square and triangular in nature. There<br/>are infinitely many square triangular numbers. To find any<br/>square triangular number, several proof and identities are<br/>discussed in this study.<br/>The proof of each property of square triangular numbers<br/>are provided together with precise illustration of each<br/>property. Proofs are analytical in nature and are<br/>concentrated in providing significant results when applied.<br/>Generation of square triangular numbers in connection<br/>with recurrence relation and Binet's Formula is established.<br/>Different properties of square triangular numbers are also given<br/>that there in complete details and with precision to show<br/>significant formulas being used to prove and propositions. <br/>This paper sought the are several theorems relationship of square <br/>triangular numbers to generating functions, Perfect Square numbers, and Pell's Equation.<br/>With regard to the forgoing goal, it is shown that there<br/>are other numbers related to Square Triangular Numbers such<br/>as Pell and Pell - Lucas Numbers. Relationship with these<br/>numbers is shown in precise manner and several proofs of<br/>these relationships are established.<br/> 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Triangular numbers<br/>Perfect squares<br/>Number theory<br/>Pell's equation