There are Infinitely Many Perrin Pseudoprimes
classification
🧮 math.NT
keywords
pseudoprimesinfinitelymanyperrinadamsalongcarmichaelclass
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This paper proves the existence of infinitely many Perrin pseudoprimes, as conjectured by Adams and Shanks in 1982. The theorem proven covers a general class of pseudoprimes based on recurrence sequences. The result uses ingredients of the proof of the infinitude of Carmichael numbers, along with zero-density estimates for Hecke L-functions.
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