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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Carmichael's conjecture on the Euler function is valid below $ 10\sp {10,000,000}$


Authors: Aaron Schlafly and Stan Wagon
Journal: Math. Comp. 63 (1994), 415-419
MSC: Primary 11A25; Secondary 11A51, 11Y11
MathSciNet review: 1226815
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Abstract: Carmichael's conjecture states that if $ \phi (x) = n$, then $ \phi (y) = n$ for some $ y \ne x$ ($ \phi $ is Euler's totient function). We show that the conjecture is valid for all x under $ {10^{10,900,000}}$. The main new idea is the application of a prime-certification technique that allows us to very quickly certify the primality of the thousands of large numbers that must divide a counterexample.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1994-1226815-3
PII: S 0025-5718(1994)1226815-3
Keywords: Euler's function, Carmichael's conjecture, prime certification
Article copyright: © Copyright 1994 American Mathematical Society