| Abstract |
Article Information:
Number of Solutions of the Equation φ (x) = 2a-1 in the Absence of Sixth Fermat Prime
Manjit Singh
Corresponding Author: Manjit Singh
Key words: Euler’s ф -function, carmichael’s conjecture, fermat primes, , , ,
Vol. 1 , (2): Page No: 30-34 |
| Submitted |
Accepted |
Published |
| 2009 Month, 00 |
2009 Sep., 02 |
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For any natural number k, J(k) is the set of solutions of the equation ф(x)=k. We find that the set of natural numbers is a disjoint union of J(k) and O(J(2a-1)) = a+1 if 1 ≤ a ≤ 32, 32 if a ≥ 33 in absence of sixth Fermat prime. Explicit expressions of J(231) and J(232) are also obtained. |
Cite this Reference:
Manjit Singh, 2009. Number of Solutions of the Equation φ (x) = 2a-1 in the Absence of Sixth Fermat Prime.
Research Journal of Mathematics and Statistics, 1(2): Page No: 30-34. |
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ISSN (Online): 2040-7505
ISSN (Print): 2042-2024 |
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