The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

When searching for an answer to the following question: What are the reasons for the reluctance of female physical education teachers in secondary schools to referee sports competitions according to the variable of years of service? It was found that the research aimed to reveal the differences between the opinions of the research sample of physical education teachers in secondary schools (girls) about refereeing sports competitions according to the variable of years of service. To achieve the research goal, it is assumed that there are significant differences between the average opinions of the research sample of female teachers and their reluctance and the reasons for the differences in the practice of refereeing sports competitions accor

Public spending represents the government’s financial leverage and has a significant impact on real and monetary economic variables, and one of these effects is the effect of public spending on the exchange rate as an important monetary variable for monetary policy, As we know that public spending in Iraq is financed from oil revenues sold in US dollars, and the Ministry of Finance converts the US dollar into Iraqi dinars to finance the government's need to spend within the requirements and obligations of the state's general budget, And converting the US dollar into Iraqi dinars has an impact on the parallel exchange market, even if there is a contractual exchange rate between the Ministry of Finance and the Central Bank of Iraq to

The researchers have discovered weaknesses in the rotational phase of the 100-meter freestyle event, including a lack of proper movement direction and control of biomechanical variables necessary for swimmers to achieve high rotational accuracy, which leads to outperforming competitors. The objective of this study was to investigate the effect of using a laser device on improving the performance of the rotational phase among swimmers on the Iraqi national team. The experimental approach was conducted on a sample of 6 swimmers, representing 100% of the target population. The researchers concluded that the utilization of a proposed laser device in the rotational phase resulted in positive differences in biomechanical variables, contri

The aim of the research is to identify the problems of teaching computer material concerning fourth grade students’ point of view in the computer department in the College of Education for Women by identifying the statistically significant differences between the answers of female students to problems in the field of school administration and in the field of teaching computer subject included the sample of research On (39) of (50) students and (78%) From the fourth grade students in the department of computer who had achieved the theoretical part in the first semester and the assembly application in the second semester in the schools of Baghdad city for the aca

The aim of this paper is to approximate multidimensional functions by using the type of Feedforward neural networks (FFNNs) which is called Greedy radial basis function neural networks (GRBFNNs). Also, we introduce a modification to the greedy algorithm which is used to train the greedy radial basis function neural networks. An error bound are introduced in Sobolev space. Finally, a comparison was made between the three algorithms (modified greedy algorithm, Backpropagation algorithm and the result is published in [16]).