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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Carmichael’s conjecture on the Euler function is valid below $10^ {10,000,000}$
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by Aaron Schlafly and Stan Wagon PDF
Math. Comp. 63 (1994), 415-419 Request permission


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
  • © Copyright 1994 American Mathematical Society
  • Journal: Math. Comp. 63 (1994), 415-419
  • MSC: Primary 11A25; Secondary 11A51, 11Y11
  • DOI:
  • MathSciNet review: 1226815