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2009 (Vol. 1, Issue: 2)
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:  Eulerís ф -function, carmichaelís conjecture, fermat primes, , , ,
Vol. 1 , (2): Page No: 30-34
Submitted Accepted Published
2009 Month, 00 2009 Sep., 02

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.
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  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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