Number Theory

    

On a Modular Property of Odd Numbers Under Tetration

Authors: Pranjal Jain

The aim of this paper is to generalize problem 3 of the 2019 PROMYS exam, which asks to show that the last 10 digits (in base 10) of t_n are same for all n >= 10, where t_0 = 3 and t_(k+1) = 3^(t_k). The generalization shows that given any positive odd integer p, t_m is congruent to t_n modulo [(p^2)+1]^n for all m >= n >= 1, where t_0 = p and t_(k+1) = p^(t_k)

Comments: 7 Pages.

Download: PDF

Submission history

[v1] 2020-10-05 21:19:37
[v2] 2020-12-31 04:59:56

Unique-IP document downloads: 334 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus