Tangent coefficient congruency



On page 9 of the link below, I solved exercise 9.9.4 of "Elementary
Number Theory" (Uspensky and Heaslet) in a manner apparently different
from what the authors intended.

As shown in the pdf, I used Kummer's result (from section 9), which is
based on Voronai's (from section 8). However, I suspect I'm missing
the power of direct use of Voronai. Also, although I suspect that
exercise 9.9.3 could be relevant, I'm stumped.

Request solution that directly uses Voronai.

Link:

http://members.cox.net/sgschooler/Exercise_9-9-4_Tangent_Coefficient_Congruency.pdf

.


Quantcast