Thomas P. Dence

Euler’s Function in Residue Classes

We discuss the distribution of integers n with φ(n) in a particular residue class, showing that if a residue class contains a multiple of 4, then it must contain infinitely many numbers p(n). We get asymptotic formulae for the distribution of p(n) in the various residue classes modulo 12.

Some Half-Row Sums from Pascal's Triangle via Laplace Transforms

Tom Dence (tdence@ashland.edu), a native of Toledo, Ohio, completed his undergraduate work at Bowling Green State University, then headed to Colorado for graduate work at the University of Colorado and Colorado State. After a post-doctoral fellowship at New Mexico State, teaching positions at Bowling Green, Southern Utah, Cal State–Los Angeles, and the University of Georgia followed. Tom is finishing his 23rd year at Ashland University (Ashland, OH 44805), and is currently serving as President of the Ohio Section of the MAA. When not golfing with his three sons, Tom enjoys gardening, photography, hiking out West, racquetball, and walking with his dog Euler.

Series of Reciprocal Triangular Numbers.

Summary Reciprocal triangular numbers have appeared in series since the very first infinite series were summed. Here we attack a number of subseries of the reciprocal triangular numbers by methodically expressing them as integrals.