2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167263We prove that the ratio of the Newman sum over numbers multiple of a fixed integer which is not multiple of 3 and the Newman sum over numbers multiple of a fixed integer divisible by 3 is o(1) when the upper limit of summing tends to infinity.We also discuss a connection of our results with a digit conjecture on primes.12 pages;improvement of factor mu_m and addition an exampleNumber Theory11A63text