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.

Abstract That the child is aged 7 years, surrounded by information, knowledge and skillsvaried, which constitute the raw material of experience teaching and is in the rule of inputlearning, if received by the student of these data are positive, these data require research and audit, the style becomes more positive, effective, and then becomes the explorer, butnot done exploration efficiency without the visual, auditory and sensory owned by thechildren. So study aimed to identify the values of the optical track and explore mathematical and find the relationship between them. And use the descriptive approach in a manner the linkon the children of the first year of primary school age (6-7) years in my school Waziriya and Karkh, during the peri

Infertilityis oneuof the most problemsathatufacingaadvancedunations. In the general, about halfof allacasesaof the infertility are causedby factors thaturelated toathe male partner. Propos educausesvofumalev infertility include evgeneticuand environmental factors. Blood samples from 64 infertileumen allawere living in urban its al-Fallujah city (30 azospermeiauand 34 oligospermeia) and 32 fertile men (asuthe control group) were collected. Heavy metal concentrations inusera of infertile and fertile groupswereumeasured by using Atomic Absorption Spectrophotometer. Y- chromosomemicrodeletions were detected by using PCR techniques. Significantdifferences (P?0.05)uin the concentration ofucopper (0.0267±0.0147 and 0.0278±0.0273, for inf

Infertilityis oneuof the most problemsathatufacingaadvancedunations. In the general, about halfof allacasesaof the infertility are causedby factors thaturelated toathe male partner. Propos educausesvofumalev infertility include evgeneticuand environmental factors. Blood samples from 64 infertileumen allawere living in urban its al-Fallujah city (30 azospermeiauand 34 oligospermeia) and 32 fertile men (asuthe control group) were collected. Heavy metal concentrations inusera of infertile and fertile groupswereumeasured by using Atomic Absorption Spectrophotometer. Y- chromosomemicrodeletions were detected by using PCR techniques. Significantdifferences (P?0.05)uin the concentration ofucopper (0.0267±0.0147 and 0.0278±0.0273, for infertileua

Complexes of Co(II),Ni(II),Cu(II)and Zn(II) with mixed ligand of 4 tributylphosphine (PBu3) were prepared in aqueous ethanol with (1:2:2) (M:L:PBu3)The prepared

Background: The main purpose of this study is to find if there is any correlation between the level of C-reactive protein (CRP) in gingival crevicular fluid with its serum level in chronic periodontitis patients and to explore the differences between them according to the probing depth. Materials and methods: Forty seven male subjects enrolled in this study. Thirty males with chronic periodontitis considered as study group whom further subdivided according to probing depth into subgroup 1 with pocket depth ≤6mm, subgroup 2 with pocket depth >6mm. The other 17 subjects considered as controls. For all subjects, clinical examination where done for periodontal parameters plaque index (PLI), gingival index (GI), bleeding on probing (BOP),

The research starts from studying the contractual budget, which is one of the modern trends in preparing public budgets, both operational and capital, in addition to meeting the requirements of the global trend to achieve sustainable growth in all fields, whether financial or non-financial, and tools for the contractual budget have been identified (participation contracts, planning Implementation, monitoring) and studying its impact in supporting sustainable development through its dimensions (economic, social, and environmental). The method of the questionnaire was adopted as a main tool in collecting information on research variables and distributing it to a sample of (70) individuals who dictate positions of professional respo

Research Summary The aim of the search for knowledge of the effect generative learning strategy in: 1 - Achievement of the second grade. 2 - Systemic thinking for the second grade students when studying the biology. The study sample increased (60) students distributed into two equal experimental and control groups. Prepare the test of 40 pieces of multiple choice type and prepare a test for systematic thinking according to three skills 1. Understand the relationships between the parts of the systemic form and complement the sentences given 2 - complement the relationships between parts of the systemic form 3. Building the systemic form. It was a search result 1- There is a difference of statistical significance (at level 0.05) between th