A great universal divisibility rule

[JM Montolio A]

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

[Nick]

Originally Posted by JM Montolio A

This rule is new. I think.JM M

It follows directly from the Binomial Theorem.

[JM Montolio A]

Not.

Is new.

[JM Montolio A]

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
----------------------------------------------------