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.

 Fusobacterium are compulsory anaerobic gram-negative bacteria, long thin with pointed ends, it causes several illnesses to humans like pocket lesion gingivitis and periodontal disease; therefore our study is constructed on molecular identification and detection of the fadA gene which is responsible for bacterial biofilm formation. In this study, 10.2% Fusobacterium spp. were isolated from pocket lesion gingivitis. The isolates underwent identification depending on several tests under anaerobic conditions and biochemical reactions. All isolates were sensitive to Imipenem (IPM₁₀) 42.7mm/disk, Ciprofloxacin (CIP₁₀) 27.2mm/disk and Erythromycin (E₁₅) 25mm/disk, respectively. 100% of

Social protection meets different aspects of the needs of vulnerable groups, such as the economic, health, education, and family relations and ties in the Iraqi society. This is because vulnerable groups have suffered from social and economic influences that have negative implications on the social reality as a whole. Poverty is a case in point, which paved the way to frequent setbacks that have led to social structure instability. Accordingly, the present study aims to examine the role and effect of the Net of Social Protection Program in equally distributing social protection to curb or mitigate any negative consequnces that might happen to the poor segments and vulnerable people, who are succeptible to shocks, such as: the orphans, un

The research tagged with (similar rulings in the holy heavenly books - the Holy Qur’an and the Bible) highlights that there are a number of rulings in the heavenly books that are similar to each other in terms of content, meaning and significance and did not change from one prophet to another because they relate to the basic interests on which social relations are built. Documenting ties, preserving rights, preventing abuse, etc. These are among the divine purposes in clarifying rulings in order to reach their goals and achieve their goals. Therefore, by combining these rulings, many problems and incidents that are the subject of disagreement and doubt between the two religions can be achieved and addressed. Those who want reform, righ

Linguistic studies present a distinguished place among modern human studies, as we find this clear in the scientific research institutions of the developed nations, it is the main pillar in the strengthening of links and consolidation pillars between individuals and groups. It is a language and between people's thoughts, feelings and actions, and has been able to show that language is not only a tool of expression but is closely linked to the intellectual, emotional and social life of these people individuals and groups.
    The derivation is a major step in Arabic in classifying formulas into weights with special morphological values; these are of great importance in sentences and structures that are the domain of the searc

The main purpose of the research is to study the significance of the event in the explicit source and its significance in the Mimi source and to explain the difference between them in the Holy Quran, especially since most linguists were not interested in what the Mime source indicates in the text, but focused on its form and form, as they defined it as the name Linguists and grammarians did not mention a difference in meaning between the explicit source and the Mimi source, and they interpret the second in the first sense, which led me to choose this topic, to know the significance of each source through Appeal to the maqam and occasion in a challenge D The exact meaning.

Abstract

The Holy Quran is the greatest motivator for the mind to keep pace with life. The doctrine of faith is a requirement of logic and wisdom, and it cannot be reached by the hand of superstition. The Qur’an destroyed the principle of superstition in the verses of the creation of the universe. The principle of inactivity of the Qur’an is a false accusation that collision with the texts of the Qur’an. The secret of scientific development is to harness the laws of nature, benefit from them, and walk according to its requirements, on which the manifestations of civilization and the Qur’an are based

In The Name of Allah Most Gracious Most Merciful

The characteristics of the doers of good are mentioned in the Holy Book of God, and love for them in five places, and whoever God loves, honors him and gives him victory. As for the love of the righteous, it has to do with loyalty, covenant, and integrity. Committing sins 0 Then after that he mentioned God those who fight in His cause and those who rely on Him and return to Him and turning away from everything else.

words of God the Quranic text , is genera words have many faces and connotations a ccording to references, cutures and Ages.That the Quranic text is fixed , But the connotations are moveable the scientists agreed about the miracle of the Qurantic text , But they differd of the Position of miracLe including the muatazala and Al- Ashaira who have adopted the idea of sytem and miracle of linguistic . Most of them were lingustics, grammerians and writers as: AL- Jahith, AL- Faraa Abivbeida , Ibn kutaba , AL -Rumani , AL -katabi , AL- Bakilaai , AL- Gargani and Others.
They also differed in what the words of Allaah mean . Is the Quranic text creature or updated ,it is the issue that exhausted the effort.of muslim scientists though its imbo

In this research, the researchers attempted to reveal the non-verbal language in the Holy Qur'an through the hurt of the eye, its communicative effect, and its psychological significance in order to demonstrate the importance of this language. Fold the search ..