David G. Radcliffe

collaborators

3 papers

math.NT2025

Elementary Bounds on Digital Sums of Powers, Factorials, and LCMs

David G. Radcliffe

We prove logarithmic lower bounds on digital sums of powers, multiples of powers, factorials, and the least common multiple of ${1, \dots, n}$ , using only elementary number theor…

math.NT2016

A product rule for triangular numbers

David G. Radcliffe

We prove that there are exactly five sequences, including the triangular numbers, that satisfy the product rule $T (mn) = T (m) T (n) + T (m - 1) T (n - 1)$ for all $m, n \geq 1$ .

math.NT2016

The growth of digital sums of powers of 2

David G. Radcliffe

We give an elementary proof that the sum of the digits of $2^{n}$ in base 10 is greater than $lo g_{4} n$ . In particular, the limit of the sum of digits of $2^{n}$ is infinite.