GPH - International Journal of Mathematics <p style="font-family: Helvetica;">The GPH Journal of&nbsp; Mathematics&nbsp;is a an open access journal which publishes research articles, reviews, case studies, guest edited thematic issues and short communications/letters in all areas of mathematics, applied mathematics, applied commutative algebra and algebraic geometry, mathematical biology, physics and engineering, theoretical bioinformatics, experimental mathematics etc.</p> GPH - International Journals en-US GPH - International Journal of Mathematics <p>Author(s) and co-author(s)&nbsp;jointly&nbsp;and severally represent and warrant that the Article is original with the author(s) and does not infringe any&nbsp;copyright or violate any other right of any third parties, and that the Article has not been published&nbsp;elsewhere.&nbsp;Author(s) agree to the terms that the <strong>GPH Journal</strong> will have the full right to remove the published article on any misconduct found in the published article.</p> Our Interesting Journey with The Fascinating Mathematics of the Closed-form Formula of Riemann zeta and eta functions <p>An explicit identity of sums of powers of complex functions presented via this a closed-form formula of Riemann zeta function produced at any given non-zero complex numbers. The closed-form formula showed us Riemann zeta function has no unique solution for any given non-zero complex numbers which means Riemann zeta function is entirely divergent. Infinitely many zeros of Riemann zeta function produced unfortunately those zeros also gives us non-zero values of Riemann zeta function. Among those zeros, some of them are zeros of Riemann hypothesis. The present paper also discussed on eta function(alternating Riemann zeta function) with exactly the same behavior as Riemann zeta function.</p> Mulatu Lemma Agegnehu Atenaand Tilahun Muche Wondimu Tekalign ##submission.copyrightStatement## 2021-02-22 2021-02-22 4 02 01 10 The Mulatu Numbers in Actions <p>The Mulatu numbers were introduced in [1]. The numbers are sequences of numbers of the form: <strong>4</strong>,<strong>1, 5,6,11,17,28,45</strong><strong>... </strong>&nbsp;The numbers have wonderful and amazing properties and patterns.</p> <p>In mathematical terms, the sequence of the Mulatu numbers is defined by the following <a href="">recurrence relation</a>:</p> <p><img src="/public/site/images/mlemma/recurrence_relation.PNG"></p> <p>The double Angel Formulas for Fibonacci and Lucas numbers are given by the following formulas respectively<strong>.</strong></p> <p><strong><img src="/public/site/images/mlemma/formulas.PNG"></strong></p> <p>Since both the Fibonacci and Lucas numbers have double angle Formulas, It is natural to ask if such formula exists for Mulatu Numbers. The answer is affirmative and produces the following paper.</p> <p><em>2000 Mathematical Subject Classification:&nbsp; 11</em></p> Mulatu Lemma Latrice Tanksley Keisha Brown ##submission.copyrightStatement## 2021-02-22 2021-02-22 4 02 11 16