In Remembrance: Lloyd Carmichael (1894-1971)
نویسندگان
چکیده
منابع مشابه
In remembrance.
“John was an inspiring teacher and experimentalist. His educational passion was creating hands-on experiments built from ordinary parts you can find at any hardware store, what he lovingly called ‘mulch,’” said MIT senior lecturer in physics, and former King student, Peter Dourmashkin ’76 (physics), ’78 (math), PhD ’84. “He was MITx before MITx.” King was born in London and educated in France, ...
متن کاملCarmichael Numbers in Arithmetic Progressions
We prove that when (a, m) = 1 and a is a quadratic residue mod m, there are infinitely many Carmichael numbers in the arithmetic progression a mod m. Indeed the number of them up to x is at least x1/5 when x is large enough (depending on m). 2010 Mathematics subject classification: primary 11N25; secondary 11A51.
متن کاملCarmichael Numbers in Number Rings
for all integers a. This result gives us the rudimentary Fermat Compositeness Test: If a 6≡ a (mod n) for some integer a, then n is composite. While this has the advantage of being computationally simple, it has the distinct disadvantage of failing for some composite n and choice of a. Take, for example, n = 341 = 31 · 11 and a = 2. A quick computation tells us that 2 ≡ 2 (mod 341). Fortunately...
متن کاملCarmichael numbers and pseudoprimes
We now establish a pleasantly simple description of Carmichael numbers, due to Korselt. First, we need the following notion. Let a and p be coprime (usually, p will be prime, but this is not essential). The order of a modulo p, denoted by ordp(a), is the smallest positive integer m such that a ≡ 1 mod p. Recall [NT4.5]: If ordp(a) = m and r is any integer such that a ≡ 1 mod p, then r is a mult...
متن کاملHigher-order Carmichael numbers
We define a Carmichael number of order m to be a composite integer n such that nth-power raising defines an endomorphism of every Z/nZalgebra that can be generated as a Z/nZ-module by m elements. We give a simple criterion to determine whether a number is a Carmichael number of order m, and we give a heuristic argument (based on an argument of Erdős for the usual Carmichael numbers) that indica...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Blue Jay
سال: 1971
ISSN: 2562-5667,0006-5099
DOI: 10.29173/bluejay3465