A Historical Survey of the Fundamental Theorem of Arithmetic

Ağargün, Ahmet; Özkan, Erdoğan Mehmet

doi:10.1006/hmat.2001.2318

Cited by 6 publications

(2 citation statements)

References 8 publications

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“…Basis I: Each composite number is expressed as the unique product of more than one prime number by the fundamental theorem of arithmetic and Book VII -proposition 31 & Book IX -proposition 14 of Euclid's Elements [2,6].…”

Section: Introductionmentioning

confidence: 99%

A Fundamental Study of Composite Numbers as a Different Perspective on Problems Related to Prime Numbers

Gocgen¹,

Aysun²

2023

Preprint

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Prime number-related issues can be viewed from drastically different perspectives by examining the close connections between prime numbers and composite numbers. We think that multiple perspectives are the pillars on the path to solutions so we have created this study. As a result of the study, we proposed two new formulas by presenting three theorems and one proof for each theorem, a total of three proofs. We proved that the formula p · n + p returns a composite number in the first of the theorems, which is the preliminary theorem. Our first theorem except the preliminary theorem is that the formula p · n + p returns all composite numbers, and we proved that too. Finally, we created Theorem II using Theorem I to use in our other work and proved that the formula 2 · n · p + p returns all odd composite numbers, which is Theorem II. Afterward, we presented the similarities of the 2 · n · p + p formula we put forth with another known formula.

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Section: Introductionmentioning

confidence: 99%

A Fundamental Study of Composite Numbers as a Different Perspective on Problems Related to Prime Numbers

Gocgen¹,

Aysun²

2023

Preprint

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show abstract

“…Basis I: Each composite number is expressed as the unique product of more than one prime number by the fundamental theorem of arithmetic and Book VII proposition 31 & Book IX -proposition 14 of Euclid's Elements (Euclid and Thomas, 1956;Göksel and Mehmet, 2001).…”

Section: Introductionmentioning

confidence: 99%

A Fundamental Study of Composite Numbers as a Different Perspective on Problems Related to Prime Numbers

Aysun¹,

Gocgen²

2023

IJPAMR

View full text Add to dashboard Cite

Prime number-related issues can be viewed from drastically different perspectives by examining the close connections between prime numbers and composite numbers. We think that multiple perspectives are the pillars on the path to solutions so we have created this study. As a result of the study, we proposed two new formulas by presenting three theorems and one proof for each theorem, a total of three proofs. We proved that the formula p • n + p returns a composite number in the first of the theorems, which is the preliminary theorem. Our first theorem except the preliminary theorem is that the formula p • n + p returns all composite numbers, and we proved that too. Finally, we created Theorem II using Theorem I to use in our other work and proved that the formula 2 • n • p + p returns all odd composite numbers, which is Theorem II. Afterward, we presented the similarities of the 2 • n • p + p formula we put forth with another known formula.

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Fermat: The Founder of Modern Number Theory

Kleiner

2011

Excursions in the History of Mathematics

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A Historical Survey of the Fundamental Theorem of Arithmetic

Cited by 6 publications

References 8 publications

A Fundamental Study of Composite Numbers as a Different Perspective on Problems Related to Prime Numbers

A Fundamental Study of Composite Numbers as a Different Perspective on Problems Related to Prime Numbers

A Fundamental Study of Composite Numbers as a Different Perspective on Problems Related to Prime Numbers

Fermat: The Founder of Modern Number Theory

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