The Saka calendrical inscriptions recorded the time journey in its own specific way, such as the use of suklapaksa and kresnapaksa, equipped with saptawara, pancawara and sadwara day names. At the next stage, it is addedd with wuku. During the Majapahit era, the time dimensional recording was expanded to include such elements as naksatra, yoga, karaṇa, muhūrta, dewatā, grahacāra, parweśa, mandala, and rāśi. This article traces the journey of usage of these time dimensions and completes it with the sculpture samples in some inscriptions from Majapahit era or after, and proposes it as the archipelago’s ethnoastronomy.
This research may provide the solutions (if any) from the Non-linear Diophantine equation (7 k — 1) x + (7 k ) y = Z 2.There are 3 possibilities to determine the solutions from the Non-linear Diophantine equation: single solution, multiple solutions, and no solution. The research method is conducted in two stages: first, using a simulation to determine the solutions (if any) from the Non-linear Diophantine equation (7 k — 1) x + (7 k ) y = z 2; second, using Catalan conjecture and characteristics of congruency theory, which is proven that the Non-k linear Diophantine equation has a single solution ( x , y , z ) = ( 1 , 0 , 7 k 2 ) for x, y, z as non-negative whole numbers and k as the positive even whole number.
Kegiatan Pengabdian Kepada Masyarakat ini bertujuan untuk meningkatkan kualitas dan motivasi pembelajaran matematika khususnya materi penjumlahan dan pengurangan bilangan bulat pada siswa PKBM Budi Luhur Pekaja Banyumas. Kegiatan pembelajaran ini dilaksanakan secara luring di awal semester gasal tahun akademik 2022/2023 dengan melibatkan siswa kelas 7 (tujuh). Metode pembelajaran yang digunakan adalah ceramah dan demonstrasi penggunaan alat peraga yang diberi nama ’papan aljabar’. Alat peraga papan aljabar merupakan alat peraga konkrit hasil pengembangan dari alat peraga semi konkrit yaitu garis bilangan yang digunakan untuk menjelaskan materi penjumlahan dan pengurangan bilangan bulat. Evaluasi keberhasilan hasil kegiatan pembelajaran didasarkan dari nilai pre test dan post test yang diberikan kepada siswa sebelum dan sesudah menggunakan alat peraga papan aljabar. Hasil evaluasi menunjukkan bahwa rata-rata nilai siswa meningkat sebesar 64,7 % untuk materi penjumlahan bilangan bulat dan 39,1 % untuk materi pengurangan bilangan bulat.
Linear Diophantine Equation is a polynomial equation with degree 1 and non-zero integer coefficient. The general form of Diophantine Linear equation with 2 variables is ax + by = c with a, b, c ϵ Z and a, b ≠ 0 . This may be stated as congruency ax ≡ b ( mod m) . Therefore, Diophantine Linear equation ax + by = c may be solved if and only if the equivalent of congruency ax ≡ b (mod m ) may be solved. If the Linear Diophantine Equation has solution, the solution will be integer pair x and y which fulfills equation ax + by = c . Differently with Non-linear Diophantine equation, there is no standard method to find the solution. There are 3 possibilities related to the solution of Diophantine equation, either linear or non-linear. The solution may be single solution, multiple solutions or no solution. This research will discuss the solution of non-linear exponential Diophantine equation 13 x + 31 y = z 2 using the congruency theory. The methods used may be simulation, literature study and journal. Using the congruency theory, it is found that Non-Linear Exponential Diophantine equation 13 x + 31 y = z 2 has no solution, for x, y, z of integers.
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