Revisited Carmichael’s Reduced Totient Function
The modified Totient function of Carmichael <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>(</mo><mo>.</mo><mo>)</mo></mrow></semanti...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/15/1800 |
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| author | Samir Brahim Belhaouari Yassine Hamdi Abdelouahed Hamdi |
| author_facet | Samir Brahim Belhaouari Yassine Hamdi Abdelouahed Hamdi |
| author_sort | Samir Brahim Belhaouari |
| collection | DOAJ |
| description | The modified Totient function of Carmichael <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>(</mo><mo>.</mo><mo>)</mo></mrow></semantics></math></inline-formula> is revisited, where important properties have been highlighted. Particularly, an iterative scheme is given for calculating the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>(</mo><mo>.</mo><mo>)</mo></mrow></semantics></math></inline-formula> function. A comparison between the Euler <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula> and the reduced totient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>(</mo><mo>.</mo><mo>)</mo></mrow></semantics></math></inline-formula> functions aiming to quantify the reduction between is given. |
| first_indexed | 2024-03-10T09:12:29Z |
| format | Article |
| id | doaj.art-d7244911977547b7ad09911f75c5b8ed |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T09:12:29Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d7244911977547b7ad09911f75c5b8ed2023-11-22T05:56:53ZengMDPI AGMathematics2227-73902021-07-01915180010.3390/math9151800Revisited Carmichael’s Reduced Totient FunctionSamir Brahim Belhaouari0Yassine Hamdi1Abdelouahed Hamdi2College of Science and Engineering, Hamad Bin Khalifa University Education City, Doha 24404, QatarApplied Mathematics Engineering, Ecole Polytechnique of Paris, 91128 Palaiseau, FranceDepartment of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, Doha 2713, QatarThe modified Totient function of Carmichael <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>(</mo><mo>.</mo><mo>)</mo></mrow></semantics></math></inline-formula> is revisited, where important properties have been highlighted. Particularly, an iterative scheme is given for calculating the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>(</mo><mo>.</mo><mo>)</mo></mrow></semantics></math></inline-formula> function. A comparison between the Euler <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula> and the reduced totient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>(</mo><mo>.</mo><mo>)</mo></mrow></semantics></math></inline-formula> functions aiming to quantify the reduction between is given.https://www.mdpi.com/2227-7390/9/15/1800Euler theoremEuler’s totient functionprime numbers |
| spellingShingle | Samir Brahim Belhaouari Yassine Hamdi Abdelouahed Hamdi Revisited Carmichael’s Reduced Totient Function Mathematics Euler theorem Euler’s totient function prime numbers |
| title | Revisited Carmichael’s Reduced Totient Function |
| title_full | Revisited Carmichael’s Reduced Totient Function |
| title_fullStr | Revisited Carmichael’s Reduced Totient Function |
| title_full_unstemmed | Revisited Carmichael’s Reduced Totient Function |
| title_short | Revisited Carmichael’s Reduced Totient Function |
| title_sort | revisited carmichael s reduced totient function |
| topic | Euler theorem Euler’s totient function prime numbers |
| url | https://www.mdpi.com/2227-7390/9/15/1800 |
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