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Tom Wright “Carmichael Numbers: Elliptic and Arithmetical”
December 11, 2017 @ 2:30 pm - 3:30 pm
Monday, Dec. 11, 2.30 pm, rm. 409 A
Prof. Tom Wright, Wofford College
Title: Carmichael Numbers: Elliptic and Arithmetical
Abstract: Carmichael numbers are numbers which satisfy a certain test for primality but are nevertheless not prime. In this talk, we discuss several new results on Carmichael numbers. First, we prove that there are infinitely many Carmichael numbers in arithmetic progressions. Second, we establish an elliptic curve analogue of Carmichael numbers called (unsurprisingly) “elliptic Carmichael numbers,” and we prove that there are infinitely many of these as well. We also discuss variants of questions about Carmichael numbers and examine some work that has been done on those.