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Chinese Hypothesis

A Prime $p$ always satisfies the condition that $2^p-2$ is divisible by $p$. However, this condition is not true exclusively for Primes (e.g., $2^{341}-2$ is divisible by $341=11\cdot 31$). Composite Numbers $n$ (such as 341) for which $2^n-2$ is divisible by $n$ are called Poulet Numbers, and are a special class of Fermat Pseudoprimes. The Chinese hypothesis is a special case of Fermat's Little Theorem.

See also Carmichael Number, Euler's Theorem, Fermat's Little Theorem, Fermat Pseudoprime, Poulet Number, Pseudoprime


Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 19-20, 1993.

© 1996-9 Eric W. Weisstein