The Primary Pretenders
Abstract
We call a composite number q such that there exists a positive integer b with bp == b (mod q) a prime pretender to base b. The least prime pretender to base b is the primary pretender qb. It is shown that there are only 132 distinct primary pretenders, and that qb is a periodic function of b whose period is the 122-digit number 19568584333460072587245340037736278982017213829337604336734362- 294738647777395483196097971852999259921329236506842360439300.
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