In Memoriam: Alexander Carmichael (1832–1912).

In memoriam: Alexander I. Klimov (1943-2013).

In Memoriam-Professor Ajit K.Padhy

No abstract available

Carmichael 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.

Carmichael 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...

Memoriam.

George W. Housner, Carl F Braun Professor of Engineering, emeritus, died after a short illness on 10 November 2008, just a few weeks before his 98th birthday. He was in the retirement home in Pasadena where he had lived for several years. For all of us who knew George, this marked the end of an era. Few people have guided and nurtured a field the way George led earthquake engineering over a per...