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Abstract
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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
Submitted: 2009 Month, 00
Accepted: 2009 Sep., 02
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Abstract:
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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.
Key words: Euler’s ф -function, carmichael’s conjecture, fermat primes, , , ,
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Cite this Reference:
Manjit Singh, . Number of Solutions of the Equation φ (x) = 2a-1 in the Absence of Sixth Fermat Prime. Research Journal of Mathematics and Statistics, (2): Page No: 30-34.
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ISSN (Online): 2040-7505
ISSN (Print): 2042-2024 |
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