mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Miscellaneous Math

Reply
 
Thread Tools
Old 2018-02-26, 19:06   #1
JM Montolio A
 
Feb 2018

9610 Posts
Smile A great universal divisibility rule

for n= 76657.
Divider, Base, Pot, product
7, 10, 3, (7,6,6,5,7)*(81,27,9,3,1)= 7*115
47, 100, 6, (7,66,57)*(36,6,1)= 47*15
233, 1000, 68, (76,657)*(68,1)= 76*68+657*1= 233*25

Note
Pot = Base mod Divider.
Product is: the number on Base, MULTIPLIED BY, the powers of Pot.

The rule is: (Divider | N) sii (Divider | Product)

This rule is new. I think.

JM M
JM Montolio A is offline   Reply With Quote
Old 2018-02-26, 22:13   #2
Nick
 
Nick's Avatar
 
Dec 2012
The Netherlands

7×239 Posts
Default

Quote:
Originally Posted by JM Montolio A View Post
This rule is new. I think.JM M
It follows directly from the Binomial Theorem.
Nick is online now   Reply With Quote
Old 2018-02-27, 11:52   #3
JM Montolio A
 
Feb 2018

25×3 Posts
Default

Not.

Is new.
JM Montolio A is offline   Reply With Quote
Old 2018-02-27, 16:11   #4
JM Montolio A
 
Feb 2018

25×3 Posts
Default

look some results:

NBP

e divisor de Me
---------------------------------------
e 11000113 div 66000679
e 11000113 div 1232012657
e 11000189 div 3762064639
e 11000293 div 1386036919
e 11000299 div 374010167
e 11000369 div 88002953
e 11000387 div 1606056503
e 11000401 div 66002407
e 11000401 div 176006417
e 11000603 div 22001207
e 11000651 div 22001303
----------------------------------------------------
JM Montolio A is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Divisibility sequences based on recurrence relations carpetpool Combinatorics & Combinatorial Number Theory 1 2017-12-21 00:42
Sieve for divisibility sequences carpetpool Information & Answers 0 2017-11-28 07:44
Should I buy The Joy of Mathematics DVD from The Great Courses? stathmk Information & Answers 14 2012-10-08 18:56
It Seems The Great Spider ... Dubslow Forum Feedback 13 2012-06-01 13:39
The Great Rebate-Card ripoff ewmayer Lounge 5 2009-09-30 01:46

All times are UTC. The time now is 09:36.

Tue May 11 09:36:48 UTC 2021 up 33 days, 4:17, 1 user, load averages: 1.57, 1.43, 1.43

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.